Risky Assets Research Articles

A mean field game approach to optimal investment and risk control for competitive insurers

We consider an insurance market consisting of multiple competitive insurers with a mean field interaction via their terminal wealth under the exponential utility with relative performance. It is assumed that each insurer regulates her risk by controlling the number of policies. We respectively establish the constant Nash equilibrium (independent of time) on the investment and risk control strategy for the finite n-insurer game and the constant mean field equilibrium for the corresponding mean field game (MFG) problem (when the number of insurers tends to infinity). Furthermore, we examine the convergence relationship between the constant Nash equilibrium of finite n-insurer game and the mean field equilibrium of the corresponding MFG problem. Our numerical analysis reveals that, for a highly competitive insurance market consisting of many insurers, every insurer will invest more in risky assets and increase the total number of outstanding liabilities to maximize her exponential utility with relative performance.

Reinsurance, investment and the rationality with a diffusion model approximating a jump model

This article investigates the optimal excess-loss reinsurance, investment, and the rationality of using a diffusion model to approximate a jump model. We assume that the instantaneous rate of return of the risky asset is modelled by an Ornstein-Uhlenbeck (O-U) process, and the insurance claims are modeled by a compound Poisson (CP) process and a diffusion approximation (DA) model. By using the stochastic dynamic programming method, the closed-form expressions for the optimal reinsurance and investment strategies and the corresponding value functions are derived. We find that the insurer with the CP claim model always has higher reinsurance demand than the insurer with the DA claim model. Moreover, the error of using the DA model to approximate the CP model is very much dependent on the reinsurance price. Numerical analysis shows that the insurer adjusts the investment strategy as the state of the financial market changes.

Quaking the stock market: Event study evidence on the Turkey-Syria earthquake

This study delves into the aftermath of the catastrophic earthquake that hit Turkey and Syria on 06 February 2023, claiming more than 50000 lives. Applying the event study method, with the market model estimation over days (−255, −1) and (0,+5) event window, to the daily returns of 382 listed firms, we show that the Turkey-Syria earthquake significantly affected the stock returns. The average abnormal return decreased from −0.79% on event day (t) to −11.04% on t+2. The cumulative impact on all the sectors (Energy (−15.98%), Utilities (−15.36%), Financials (14.92%), Consumer non-cyclicals (−14.46%), Technology (−14.38%), Industrials (−12.40%), Consumer cyclicals (−12.12%), Real Estate (−11.51%), Health Care (−11.18%)), except Basic Materials (4.63%), has been negative. The cross-sectional examination negates the size anomaly that small firms outperform large firms. Larger firms and those with less volatile stocks tend to be more resilient, whereas riskier firms experience more significant losses. These findings suggest that firms diversify their portfolios to include less risky assets or take steps to reduce volatility in their stock prices.

Banking regulation with risk of sovereign default

Banking regulation routinely designates domestic government debt as safe, even when this debt is risky. We show, in a parsimonious model, that this failure to recognize the riskiness of government debt induces domestic banks to “gamble” with depositors’ funds by purchasing risky government bonds and assets correlated with them. Sovereign defaults then result in banking crises; however, by permitting banks to gamble, the regulator lowers the government’s borrowing costs ex-ante. Thus, the government has an incentive to ignore the riskiness of the sovereign bonds. We derive a set of testable implications and present supporting empirical evidence from sovereign debt crises in Russia, Argentina, and the Eurozone.

Time and frequency spillovers and drivers between rare earth and energy, metals, green, and agricultural markets

This study investigates the time and frequency return and volatility spillover relationship between rare earth markets and oil, clean energy, gold, base metal, green bond, ESG, and agricultural markets by adopting the spillover indices introduced by Diebold and Yilmaz (2014) and Baruník and Křehlík (2018). As a more comprehensive view of the spillover relationship between rare earth and these industries, this study fills the gap in the existing literature on the relationship between rare earth and energy, metals, or green-related markets. Moreover, we conduct a regression analysis to reveal the drivers of the connectedness network. The empirical results suggest that the rare earth metals (REM) market is a net spillover receiver from the base metal, clean energy, and ESG markets, which are the top three net risk emitters. The network connectedness results shed light on the connections and strengths at different time horizons throughout the sample. The regression results indicate that financial condition and investor sentiment play the most significant roles in driving connectedness and have different effects at different frequencies. Furthermore, severe financial stress may increase short-term risk spillover, which indicates that investors sell out risky assets in stressful times. However, financial stress decreases long-term spillover, which implies that it damages the long-term operation of the financial market. The results could guide investors holding REM assets to balance risk and return and also provide references for policymakers to monitor market conditions and adopt policies to foster the health of the REM market.

Vine copula‐based scenario tree generation approaches for portfolio optimization

AbstractThis paper presents an efficient heuristic to generate multi‐stage scenario trees for portfolio selection problems. In the case of two or more risky assets, investors need to account for the complex multivariate dependence among different assets. The dependence patterns have shown not only asymmetric and fat tails but also time‐varying, and the upper and lower tails have different effect on portfolio management. In this paper, we design a new scenario generation method by combining the GARCH‐type model and vine copula model to properly reflect these complex dependence patterns in multiple assets in a flexible way. A multi‐stage scenario tree is generated sequentially from this model by simultaneously utilizing the simulation and clustering methods. The scenarios' nodal probabilities are determined by solving an improved moment matching model, whose objective is to maintain the central moments and lower tails of the original distribution. The resulting scenario trees are then tested on a multi‐stage portfolio selection model. The experimental results prove the efficiency and advantages of our proposed scenario generation method over other existing models or methods and the positive influence of moment matching on our method.

Multiportfolio Optimization: A Fairness-Aware Target-Oriented Model

Problem definition: We consider a multiportfolio optimization problem in which nonlinear market impact costs result in a strong dependency of one account’s performance on the trading activities of the other accounts. Methodology/results: We develop a novel target-oriented model that jointly optimizes the rebalancing trades and the split of market impact costs. The key advantages of our proposed model include the consideration of clients’ targets on investment returns and the incorporation of distributional uncertainty. The former helps fund managers to circumvent the difficulty in identifying clients’ utility functions or risk parameters, whereas the latter addresses a practical challenge that the probability distribution of risky asset returns cannot be fully observed. Specifically, to evaluate the quality of multiple portfolios’ investment payoffs in achieving targets, we propose a new class of performance measures, called fairness-aware multiparticipant satisficing (FMS) criteria. These criteria can be extended to encompass distributional uncertainty and have the salient feature of addressing the fairness issue with the collective satisficing level as determined by the least satisfied participant. We find that, structurally, the FMS criteria have a dual connection with a set of risk measures. For multiportfolio optimization, we consider the FMS criterion with conditional value-at-risk being the underlying risk measure to further account for the magnitude of shortfalls against targets. The resulting problem, although nonconvex, can be solved efficiently by solving an equivalent converging sequence of tractable subproblems. Managerial implications: For the multiportfolio optimization problem, the numerical study shows that our approach outperforms utility-based models in achieving targets and in out-of-sample performance. More generally, the proposed FMS criteria provide a new decision framework for operational problems in which the decision makers are target-oriented rather than being utility maximizers and issues of fairness and ambiguity should be considered. Funding: This work was supported by the Hong Kong Research Grants Council [Grants 14210821, 16204521], Leading Talent Program of Guangdong Province [Grant 2016LJ06D703], and the National Natural Science Foundation of China [Grants 71971187, 72171156, 72231002, 72331009]. Supplemental Material: The online appendix is available at https://doi.org/10.1287/msom.2021.0363 .

Forward starting options pricing under a regime-switching jump-diffusion model with Wishart stochastic volatility and stochastic interest rate

Vanilla options become effective immediately after they are entered, while some exotic options will only come to effective some time after they are bought or sold. Forward starting options are one kind of such exotic options started actually at some pre-specified future date. This paper presents an extension of regime-switching jump diffusion model, in which the parameters are driven by a continuous time and stationary Markov chain on a finite state space, by introducing the Wishart process into the instantaneous variance-covariance matrix of the risky asset price and stochastic interest rate. We derive the discounted conditional joint characteristic function and the forward characteristic function of the log-asset price and its the instantaneous variance-covariance process, and thereby the price of forward starting options are well evaluated by the probabilistic approach combined with the Fourier-cosine (COS) method. We also provide efficient Monte Carlo simulation of this proposed model, and simulated solutions to forward starting options pricing within a two-state regime switching framework. Numerical results show that the COS method is accurate and efficient for pricing forward starting options. Finally, we analyse impacts of some main parameters (especially, parameters in the Wishart stochastic volatility) in this proposed model on option prices and Δ values. Also, we consider the forward implied volatility. Furthermore, the forward starting options under the regime-switching jump diffusion model with Wishart stochastic volatility and stochastic interest rate which we derived are more generalized than those recently appeared in the derivatives pricing literature, and thus have wider application.

Stock Performance Analysis of PT. Kalbe Farma TBK (KLBF) in 2016-2020

When the World Health Organization (WHO) announced that COVID-19 was upgraded to pandemic status, investors began to reconsider their portfolio structure from risky assets such as stocks to gold. This study aims to determine the stock performance of PT. Kalbe Farma Tbk during the COVID-19 pandemic. A quantitative descriptive approach by linking company financial statement data with the phenomenon of the COVID-19 pandemic is the method used in this study. Based on the results of the research that has been done, it can be concluded that the performance of PT. Kalbe Farma Tbk before and during the COVID-19 pandemic on the dependent variable (stock return), namely the Current ratio, had a significant effect on Stock Return. However, based on the results of hypothesis testing regarding the effect of Earnings Per Share and Net profit margin on Stock Return partially, it can be concluded that these variables do not have a significant effect on Stock Return. Based on the conclusions above, the researcher recommends that the first company is expected to make the value of CR better in order to attract investors in investing their funds. Because if the company has a high CR value then the company can be said to have no constraints to pay its debts, thus many investors will be interested in investing in pharmaceutical sector companies and that can be very profitable for the company. Next is advice for those who want to invest in pharmaceutical companies, it is recommended to look at the CR owned by the company if investors want to make long-term investments.

Optimal investment problem for a hybrid pension with intergenerational risk-sharing and longevity trend under model uncertainty

This paper studies the optimal investment problem for a hybrid pension plan under model uncertainty, where both the contribution and the benefit are adjusted depending on the performance of the plan. Furthermore, an age and time-dependent force of mortality and a linear maximum age are considered to capture the longevity trend. Suppose that the plan manager is ambiguity averse to the financial market and is allowed to invest in a risk-free asset and a risky asset. The plan manager aims to find optimal investment strategies and optimal intergenerational risk-sharing arrangements by minimizing the unstable contribution risk, the unstable benefit risk and the discontinuity risk under the worst-case scenario. By applying the stochastic optimal control approach, robust optimal strategies are derived under the worst-case scenario for a penalized quadratic cost function. Through numerical analysis and three special cases, we find that the intergeneration risk-sharing is achieved in our collective hybrid pension plan effectively. And it also shows that when people live longer, postponing the retirement seems a reasonable way to alleviate the stress of the aging problem.

Prospect theory and asset allocation

We study the asset allocation of an investor with prospect theory (PT) preferences. First, we solve analytically the two-asset problem of the PT investor for one risk-free and one risky asset and find that the reference return and the level of risk aversion or risk seeking (diminishing sensitivity) affect differently less ambitious and more ambitious investors: the less ambitious investor decreases her exposure to the risky asset when increasing her reference return or the level of diminishing sensitivity, while the more ambitious investor increases her exposure to the risky asset when increasing her reference return or the level of diminishing sensitivity. However, both less and more ambitious investors decrease their exposures to the risky asset when increasing their degrees of loss aversion. In a comprehensive sensitivity analysis, we investigate how different aspects of the PT investor’s preferences contribute to her risk taking, performance and happiness. We observe, for instance, that the investor’s happiness decreases with her increasing level of ambition. Second, we perform simulations to examine concrete solutions of the theoretical two-asset problem for different types of the PT investor and for different characteristics of the risky asset and find that the assumption of skewness, as opposed to symmetry, changes the optimal investment in the risky asset. Third, we empirically investigate the performance of a PT portfolio when diversifying among a stock market index, a government bond and gold, in Europe and the US. We focus on investors with PT preferences under different scenarios regarding the reference return and the degree of loss aversion and compare their portfolio performance with the performance of investors under mean–variance (MV), linear loss averse and CVaR preferences. We find that, in the US, PT portfolios significantly outperform MV portfolios (in terms of returns) in most cases.

Optimal portfolio strategy of wealth process: a Lévy process model-based method

This paper is concerned with the optimal portfolio problem for a company that can invest in two risky assets, where a novel Lévy-process-driven model is constructed to describe the dynamics of the wealth process by using a constant elasticity of variance model and a jump-diffusion process. A delicately designed value function is proposed under the mean–variance criterion to reflect the optimal portfolio for the stochastic volatility model. By using the verification theorem, the desired optimal portfolio strategy is proposed by the solution to certain Hamilton–Jacobi–Bellman equations. Furthermore, the corresponding expressions are achieved by using the stochastic analysis theory. Finally, a numerical simulation example is provided to verify the effectiveness of the proposed optimal portfolio strategy.

Optimal mean-variance investment and reinsurance strategies with a general Lévy process risk model

This paper is concerned with the optimal time-consistent investment and reinsurance strategies for mean-variance insurers with a general Lévy Process model. Expressly, the insurers are allowed to purchase proportional reinsurance and invest in a financial market, where the surplus of the insurers is assumed to follow a Cramér–Lundberg model and the financial market consists of one risk-free asset and one risky asset whose price process is driven by a general Lévy process. Through the verification theorem, the closed-form expressions of the optimal strategies under the mean-variance criterion are derived by a complex partial integral differential Hamilton–Jacobi–Bellman equations. Finally, numerical simulations are provided to verify the effectiveness of the proposed optimal strategies and some economic interpretations are drawn.

Hedging, optimal capital structure and incentives for risk-shifting with preferences for liquidity

We develop a dynamic incomplete-markets model of entrepreneurial firms and demonstrate the implications of preferences for liquidity to entrepreneur's interdependent consumption, portfolio allocation, hedging and financing decisions. The numerical results provide several important implications. Preferences for liquidity reduce hedging demand using risky assets. Besides, the existence of preferences for liquidity decreases the implied equity value and encourages the entrepreneur to issue more debt. Especially, the preferences for liquidity can overturn the risk-shifting incentives of a risk-averse entrepreneur.

Non-zero-sum reinsurance and investment game under thinning dependence structure: mean–variance premium principle

This paper considers a non-zero-sum stochastic differential reinsurance and investment game between two competitive insurers under the expected exponential utility. It is assumed that the surplus process of each insurer is characterized by a compound Poisson model and their claim businesses are correlated through thinning dependence structure. Each insurer can purchase proportional reinsurance and is allowed to invest in a risk-free asset and a risky asset. The insurers compete with each other and are concerned with the relative performance. By using the stochastic control technique, not only the existence and uniqueness of the optimal strategies are proved, but also the specific analyses for the constraint reinsurance strategies are provided. We find that (i) the thinning dependence structure has significant impact on optimal reinsurance strategies for both insurers and can help them reduce risks; (ii) the behavior of non-zero-sum game will reduce the proportion of purchasing reinsurance for each insurer.

A Stackelberg–Nash equilibrium with investment and reinsurance in mixed leadership game

In this paper, we investigate the optimal reinsurance and investment problem from joint interests of the insurer and the reinsurer in the framework of the mixed leadership game, where both of them can invest their wealth in the financial market, and the liabilities are correlated with the risky asset. More specifically, we assume that the insurer is the leader to determine the amount he/she invests into the risky asset but acts as the follower to decide the optimal reinsurance retention level, while the reinsurer is the leader to set the reinsurance premium price and acts as a follower to determine his/her investment strategy. Both the insurer and the reinsurer aim to maximize the expected utility of their terminal wealth, and the explicit Stackelberg-Nash equilibrium is derived by solving the corresponding Hamilton-Jacobi-Bellman (HJB) equations. In order to better understand the effect of the mixed leadership game on the optimal reinsurance and investment problem, we also consider the optimization problem within the framework of the stochastic Stackelberg differential game shown in [Bai, Y., Zhou, Z., Xiao, H., Gao, R. & Zhong, F. (2021). A Stackelberg reinsurance-investment game with asymmetric information and delay. Optimization 70(10), 2131–2168.], where the reinsurer is the leader while the insurer acts as the follower for both the reinsurance and investment strategies. Some theoretical analyses and numerical examples are provided to show the economic intuition and insights of the results.

Comparing the Performance of the Expected Returns of Cryptocurrencies Using CAPM and D-CAPM Approaches

The present study compares the expected returns of cryptocurrencies using the capital asset pricing and the downside capital asset pricing models. For this purpose, fifty cryptocurrencies were studied as representative of risky assets during the five-year from 2018 to 2022 with daily frequency. Using the conditional variance test, eighteen cryptocurrencies were accepted and the rest were homogeneously rejected in the variance heterogeneity test. Among the eighteen cryptocurrencies, nine were randomly selected as the portfolio, including high-volatility, low-volatility, and medium-volatility cryptocurrencies. First, using the t-Student statistic, the total return and downside return were compared. Results showed that the capital asset pricing model and the downside risk asset pricing model can be fitted in cryptocurrencies. Using the Wald-Fisher model, we investigated the justification for selecting a more appropriate model based on downside returns. The results of the research showed that D-CAPM and CAPM show the relationship between risk and return in cryptocurrencies appropriately, and the portfolios obtained from the mentioned models show the efficiency of the two models in the cryptocurrency market.

The Impact of Supplementary Pension on Household Risky Financial Asset Allocation

With increasingly serious aging problem in China, supplementary pension, as the second pillar of the endowment insurance system, is expected to play an important role to relieve the pension pressure. Nowadays, people in China are exposed to various investment tools, but they still prefer to invest in risk-free financial assets. The allocation of household financial assets is not diversified enough. While supplementary pension is expected to improve financial structure of households. It may enhance the anti-risk ability of households, rational allocation of household assets, the ability of value-adding, and thus reduce the pressure of society to cope with the aging population. This paper selects the 2019 China Household Finance Survey (CHFS) database, using STATA software to investigate the impact of supplementary pension on risky financial asset allocation of Chinese households by applying probit and tobit models. The results show that supplementary pension can significantly increase the willingness of households to purchase risky financial products but has no significant effect on increasing the proportion of risky assets being held.

Asset allocation via life-cycle adjusted PPI strategy: evidence from the U.S. and China stock market

ABSTRACT In this article, we extend the Proportion Portfolio Insurance (PPI) strategy by a life-cycle adjusted multiplier to adapt to the scenario of multi-period investment with continuous cash inflows, such as variable annuity with minimal guarantees. Using variational methods, we establish the closed-form optimal risk multiplier that determines the proportion of risky assets. It is negatively correlated with the life-cycle phase and previous performance but positively correlated with market conditions. We test the effectiveness of the life-cycle adjusted PPI strategy in a discrete-time framework for application considerations. In the U.S. and China stock markets, the life-cycle strategies outperform benchmark strategies under various measurements with robust results. Variable annuity investors who are less risk-averse or accept a lower guarantee ratio can benefit most from our strategy.

Development of a toolkit for assessing the functional purpose of assets of commercial organizations: theoretical and methodological aspect.

To objectively determine the role of assets in the business of commercial organizations, to measure their value, it is important to disclose their functional purpose and use the appropriate tools for its evaluation. Goal. The purpose of the study is to substantiate and develop tools for assessing the functional purpose of assets of commercial organizations. In the course of the research, the works of Russian and foreign authors were studied, classified into those who identify assets and financial resources (N.I. Berzon, I.A. Blank, G.S. Gabidenova, A. Damodaran, V.V. Kovalev, V.V. Korshunov, M.V. Livson, M.R. Matthews, M.H.B. Perera, M.A. Eskindarov) commercial organizations, and vice versa. Recognition of assets as an independent economic category necessitates the formation of tools for their assessment in commercial corporate organizations. Based on the analysis of debatable aspects, the functional purpose of assets of commercial organizations is determined, including: measurement of the value of the organization’s economic turnover; characteristics of accumulated potential; participation of assets in achieving sustainable capital formation; protection against the risk of loss of liquidity by highly liquid assets exceeding the min mark, guaranteeing the safety margin of equity; production; influence on the level of risky activity of the organization; direct participation in the assessment of its financial condition. As a result, a methodological toolkit for assessing their functional purpose has been developed, which provides for the distribution of the established ranges of values of financial indicators describing the functional role of assets by phases of the economic cycle (the participation of assets in achieving sustainable capital formation – the stability of sources of asset formation, financial tension, autonomy; production – indicators of turnover and profitability of assets; influence on the level of risk activity – capital multiplier, the share of the most risky and non-performing assets in their total aggregate, etc.) based on the professional judgment of specialists.