Regime-switching Environment Research Articles

Equilibrium strategies in a defined benefit pension plan game with regime switching

This paper studies the optimal management of an aggregated overfunded pension plan of defined benefit type as a stochastic differential game in a Markovian regime-switching environment. In this asymmetric two-player game, the worker participants act collectively as a single player that claims a share of the surplus, and the sponsoring firm acts as the player who cares about the investment of the surplus fund assets. We formulate the game model in two scenarios, and use the dynamic programming technique to derive the coupled Hamilton-Jacobi-Bellman equations in each scenario. Furthermore, we propose an efficient algorithm that incorporates a kind of quasi-Newton method and the Runge-Kutta scheme to obtain the equilibrium strategies. Finally, we employ a numerical example to verify our algorithm and analyze the impact of model parameters.

Gerber-Shiu theory for discrete risk processes in a regime switching environment

In this paper we develop the Gerber-Shiu theory for the classic and dual discrete risk processes in a Markovian (regime switching) environment. In particular, by expressing the Gerber-Shiu function in terms of potential measures of an upward (downward) skip-free discrete-time and discrete-space Markov Additive Process (MAP), we derive closed form expressions for the Gerber-Shiu function in terms of the so-called (discrete) Wv and Zv scale matrices, which were introduced in [27]. We show that the discrete scale matrices allow for a unified approach for identifying the Gerber-Shiu function as well as the value function of the associated constant dividend barrier problems.

European option pricing with market frictions, regime switches and model uncertainty

The impact of market frictional costs on pricing insurance and financial products in a regime-switching environment has not been well-explored. This paper introduces a general pricing model for European options which incorporates market frictional costs, regime switches and model uncertainty. Regime switches are due to changes in an economic environment. Model uncertainty is attributed to misspecification of transition intensities for economic regimes. The selling and buying prices of a European option are determined through stochastic optimal control and nonlinear partial differential equations. A fair value is determined by a closed-form solution to a minimization problem based on a relative entropy. The fair value is consistent with the one obtained using the Esscher transform, which is an important tool in actuarial science. Numerical methods and results for implementing the pricing model are presented. The results indicate that after controlling for the model uncertainty, market frictional costs are more significant than regime switches in accounting for the fair, selling and buying prices.

An efficient algorithm for pricing reinsurance contract under the regime-switching model

This paper suggests a new and efficient variance reduction technique based on the Monte-Carlo simulation method for pricing the reinsurance contract in a regime-switching environment. The proposed approach extends the standard antithetic variables method to K>2 antithetic variables per replication of the Monte-Carlo simulation. Since the model under the regime-switching framework describes a market with arbitrage opportunities, a risk-neutral measure by Esscher transform is provided. Under this probability measure, the proposed estimator is unbiased for pricing the reinsurance contract and increasing K which leads to more variance reduction. Finally, the success of the introduced method is confirmed numerically, and the efficacy of contract parameters is evaluated on its price.

Optimal dividends under Markov-modulated bankruptcy level

This paper proposes and studies an optimal dividend problem in which a two-state regime-switching environment affects the dynamics of the company's cash surplus and, as a novel feature, also the bankruptcy level. The aim is to maximize the total expected profits from dividends until bankruptcy. The company's optimal dividend payout is therefore influenced by four factors simultaneously: Brownian fluctuations in the cash surplus, as well as regime changes in drift, volatility and bankruptcy levels. In particular, the average profitability can assume different signs in the two regimes. We find a rich structure of the optimal strategy, which, depending on the interaction of the model's parameters, can be either of barrier-type or of liquidation-barrier type. Furthermore, we provide explicit expressions of the optimal policies and value functions. Finally, we complement our theoretical results by a detailed numerical study, where also a thorough analysis of the sensitivities of the optimal dividend policy with respect to the problem's parameters is performed.

Uncertainty Measures and Sector-Specific REITs in a Regime-Switching Environment

In this paper, we attempt to explore the effects of various uncertainty measures – namely, implied volatility (VIX), tail risk (SKEW), economic policy uncertainty (EPU) and partisan conflict (PCI) indices-, on U.S. REITs returns at sector level, using the non-linear Markov regime-switching model. Our empirical results reveal that uncertainty measures have regime-dependent impacts and do not affect the return dynamics of REIT sectors in a uniform way. Office and hotel & lodging REITs exhibit the strongest sensitivity to VIX and EPU, respectively, during bearish market periods. While residential REITs are the most resilient to uncertainties, healthcare REIT returns are negatively affected from all the uncertainty factors only in the low variance regime. Hence, our findings show evidence of asymmetric, non-linear and sector-dependent linkages between REITs and uncertainties. These results provide valuable insights and important implications for REIT investors.

The links between gold, oil prices and Islamic stock markets in a regime switching environment

This paper investigates the linkages between gold, oil prices and Islamic stock market for the turbulent period 1996–2020 which covers the recent COVID-19 pandemic crisis. The paper applies standard VAR and Markov switching VAR models. Empirical results can be summarized as follows: (i) There are some significant relationships between the considered markets. (ii) The sign of the links varies significantly according to markets and regimes. (iii) There is a significant and positive link between oil and Islamic stock markets namely during turbulent periods suggesting the financialization of the crude oil market. (iv) The negative or the absence of relationships between gold market and both oil and Islamic stock markets indicate that gold can act as a hedge and safe haven during extreme market conditions. These findings have several practical implications for risk-management and portfolio diversification strategies.

Ruin probabilities for risk process in a regime-switching environment

In this paper we give a few expressions and asymptotics of ruin probabilities for a Markov modulated risk process for various regimes of a time horizon, initial reserves and a claim size distribution. We also consider a few versions of the ruin time.

Coexistence and exclusion of competitive Kolmogorov systems with semi-Markovian switching

<p style='text-indent:20px;'>This work investigates the dynamics of competitive Kolmogorov systems formulated in a semi-Markov regime-switching framework. The conditional holding time of each environmental regime is allowed to follow arbitrary probability distribution on the nonnegative half-line in the sense of approximations. Sharp sufficient conditions of the coexistence and competitive exclusion of species are established, and in the case of species coexistence, the convergence rate of the transition probability to the unique stationary measure is estimated. In weaker conditions, these results extend the existing results to the semi-Markov regime-switching environment. Particularly, the method of proving the exponential convergence of the transition probability to the invariant measure for the population models formulated as random differential equations driven by a semi-Markov process is proposed.

Robust optimal R&D investment under technical uncertainty in a regime-switching environment

ABSTRACT In this paper, we extend the classic optimal research and development (R&D) investment model into the regime-switching environment. We formulate a robust model to obtain the maximal net value function of the R&D project under a family of real-world measures, which can also be regarded as a stochastic differential game. Then, the verification argument is provided. Though we do not find the closed-form solution, we give a numerical simulation to further study the qualities of the solution to our model.

Stochastic differential games for optimal investment problems in a Markov regime-switching jump-diffusion market

We apply dynamic programming principle to discuss two optimal investment problems by using zero-sum and nonzero-sum stochastic game approaches in a continuous-time Markov regime-switching environment within the frame work of behavioral finance. We represent different states of an economy and, consequently, investors’ floating levels of psychological reactions by a D-state Markov chain. The first application is a zero-sum game between an investor and the market, and the second one formulates a nonzero-sum stochastic differential portfolio game as the sensitivity of two investors’ terminal gains. We derive regime-switching Hamilton–Jacobi–Bellman–Isaacs equations and obtain explicit optimal portfolio strategies with Feynman–Kac representations of value functions. We illustrate our results in a two-state special case and observe the impact of regime switches by comparative results.

Fishery management in a regime switching environment: Utility theory approach

In this paper, we study the problem of optimal fishing for regime switching in the growth dynamics of a given fish species which is described by the differential stochastic logistic model with two states: prior or during floods and after. The resulting dynamic programming principle leads to a system of two variational inequalities. By using viscosity solutions approach, we prove the existence and uniqueness of the value functions. Then numerical approximation of the obtained system is used to determine the optimal fishing effort for a sustainable fishery.

Optimal investment-reinsurance policy with regime switching and value-at-risk constraint

This paper studies an optimal investment-reinsurance problem for an insurance company which is subject to a dynamic Value-at-Risk (VaR) constraint in a Markovian regime-switching environment. Our goal is to minimize its ruin probability and control its market risk simultaneously. We formulate the problem as an infinite horizontal stochastic control problem with the constrained strategies. The dynamic programming technique is applied to derive the coupled Hamilton-Jacobi-Bellman (HJB) equations and the Lagrange multiplier method is used to tackle the dynamic VaR constraint. Furthermore, we propose an efficient numerical method to solve those HJB equations. Finally, we employ a practical example from the Korean market to verify the numerical method and analyze the optimal strategies under different VaR constraints.

The impacts of global economic policy uncertainty on stock market returns in regime switching environment: Evidence from sectoral perspectives

AbstractThis study contributes in building emerging literature by investigating the impacts of global economic policy uncertainty on Malaysian sectoral stock performance. This study models sectoral stock returns as time‐varying transition probability Markovian processes and employs two‐stage Markov‐switching model for findings impacts of global economic policy uncertainty on sectoral stock returns in regime switching environment. The empirical results reveal that linear framework unable to detect the effects global economic policy uncertainty, and the Markov‐switching model exhibits significant effects of global economic policy uncertainty on all sectoral stock returns excluding technology sector in Malaysia stock market. The findings also expose that the effects of global economic policy uncertainty vary across regime states, sectors, and nature of effects, where the negative effects of global economic policy uncertainty dominate over positive effects. The global economic policy uncertainty exhibits greater impacts on stock returns in high‐volatility regime. Thus, the findings confirm the existence of asymmetric, nonlinear, nonmonotonic, and state‐dependent relationship between global economic policy uncertainty and sectoral stock returns in Malaysia. Therefore, the overall empirical findings can be applied in asset pricing and investment decision‐making purposes. The findings also suggest that global economic policy uncertainty can be a systemic risk factor and predictor of stock market returns.

Threshold dynamics and ergodicity of an SIRS epidemic model with semi-Markov switching

This work studies the threshold dynamics and ergodicity of a stochastic SIRS epidemic model with the disease transmission rate driven by a semi-Markov process. The semi-Markov process used in this paper for describing a randomly changing environment is a very large extension of the most common Markov regime-switching process. We define a basic reproduction number for the semi-Markov regime-switching environment and show that its position with respect to 1 determines the extinction or persistence of the disease. In the case of disease persistence, we give mild sufficient conditions for ensuring the existence and absolute continuity of the invariant probability measure. Under the same conditions, we also prove the global attractivity of the Ω-limit set of the system and the convergence in total variation norm of the transition probability to the invariant measure. Compared with the existing results in the Markov regime-switching environment, the results generalized require almost no additional conditions.

Optimal portfolios with maximum Value-at-Risk constraint under a hidden Markovian regime-switching model

This paper studies an optimal portfolio selection problem in the presence of the Maximum Value-at-Risk (MVaR) constraint in a hidden Markovian regime-switching environment. The price dynamics of n risky assets are governed by a hidden Markovian regime-switching model with a hidden Markov chain whose states represent the states of an economy. We formulate the problem as a constrained utility maximization problem over a finite time horizon and then reduce it to solving a Hamilton–Jacobi–Bellman (HJB) equation using the separation principle. The MVaR constraint for n risky assets plus one riskless asset is derived and the method of Lagrange multiplier is used to deal with the constraint. A numerical algorithm is then adopted to solve the HJB equation. Numerical results are provided to demonstrate the implementation of the algorithm.

Risk-based optimal investment and proportional reinsurance of an insurer with hidden regime switching

In this paper, we study the optimal investment and proportional reinsurance strategy for an insurer in a hidden Markov regime-switching environment. A risk-based approach is considered, where the insurer aims at selecting an optimal strategy with a view to minimizing the risk described by a convex risk measure of its terminal wealth. We solve the problem in two steps. First, we employ the filtering theory to turn the optimization problem with partial observations into one with complete observations. Second, by using BSDEs with jumps, we solve the problem with complete observations.

Pricing dynamic fund protections with regime switching

This paper deals with the valuation of dynamic fund protections in a Markov regime-switching environment. The volatility switches over time subject to a continuous-time Markov chain. Using a regime-switching diffusion process to describe the primary mutual fund value, explicit solutions of the Laplace transforms of the value of the dynamic fund protection are obtained through martingale technique. Moreover, we analyze the value of dynamic fund protections under a generalized regime-switching jump diffusion model. Due to the complexity of Markov regime-switching, the jump process involved, and the nonlinearity, closed-form formulas for dynamic fund protection prices are virtually impossible to obtain. We design a numerical algorithm according to the Markov chain approximation techniques and obtain numerical results of the value of dynamic fund protection.

Interactions between real economic and financial sides of the US economy in a regime-switching environment

This objective of this study is to examine the linkages between real (economic) and financial variables in the United States in a regime-switching environment that accounts explicitly for high volatility in the stock market and high stress in financial markets. Since the linearity test shows that the linear model should be rejected, we employ the Markov-switching VECM to examine the same objective using the Bayesian Markov-chain Monte Carlo method. The regime-dependent impulse response function (RDIRF) highlights the increasing importance of the financial sector of the economy during stress periods. The responses and their fluctuations are significantly greater in the high-volatility regime than in the low-volatility regime.

On a Markov chain approximation method for option pricing with regime switching

In this paper, we discuss a Markov chain approximation method to price European options, American options and barrier options in a Markovian regime-switching environment. The model parameters are modulated by a continuous-time, finite-state, observable Markov chain, whose states represent the states of an economy. After selecting an equivalent martingale measure by the regime-switching Esscher transform, we construct a discrete-time, inhomogeneous Markov chain to approximate the dynamics of the logarithmic stock price process. Numerical examples and empirical analysis are used to illustrate the practical implementation of the method.