VaR Constraint Research Articles

Arbitrage with financial constraints and market power

I study how (VaR-based) financial constraints affect liquidity and welfare under different structures of the arbitrage industry. When capital is dispersed across competitive arbitrageurs, financial constraints may impair their ability to provide liquidity, lowering other investors' welfare. However, when capital is concentrated among arbitrageurs with market power, introducing constraints can make everyone better off and increase liquidity. Further, alternative constraints (fixed margins, position limits) have the same effects as VaR constraints when arbitrageurs are competitive, but not when they have market power. These results lead to new policy implications for margin and capital requirements and yield new empirical predictions.

An Interval-Valued Fuzzy Portfolio Decision Model with Entropy and VaR Constraints

An Interval-Valued Fuzzy Portfolio Decision Model with Entropy and VaR Constraints

Optimal investment based on relative performance and time-varying reference point under VaR and position constraints

Optimal investment based on relative performance and time-varying reference point under VaR and position constraints

Precommitted Strategies with Initial-time and Intermediate-time VaR Constraints

Precommitted Strategies with Initial-time and Intermediate-time VaR Constraints

DG Allocation in Distribution Networks with Considering of Voltage Stability Improvement and Loss Reduction

The improvement of the line Load-ability (LL) for voltage stability establishes the main criterion for distribution networks. The Distributed Generation (DG) resources play an important role in the supply of active and reactive power loads, bus voltage profiles, and voltage stability in distribution systems. In this paper, a new technique has been proposed for optimization of the location placement and sizing of DGs, considering the Generalized voltage Stability Index (GSI) to determine the maximum load-ability. Also, an analytical method has been applied to infer the effects of DGs on the distribution systems’ characteristics. The study also considers three types of DG modes, which are voltage control mode (PV mode), constant power mode (PQ mode), and also voltage control mode with reactive power constraint (PV mode with VAR constraint). The proposed method is applied to 12-bus, modified 12-bus, 69-bus and 94-bus radial distribution systems.

Optimal Expected Utility of Dividend Payments with Proportional Reinsurance under VaR Constraints and Stochastic Interest Rate

In this paper, we consider the problem of maximizing the expected discounted utility of dividend payments for an insurance company taking into account the time value of ruin. We assume the preference of the insurer is of the CRRA form. The discounting factor is modeled as a geometric Brownian motion. We introduce the VaR control levels for the insurer to control its loss in reinsurance strategies. By solving the corresponding Hamilton-Jacobi-Bellman equation, we obtain the value function and the corresponding optimal strategy. Finally, we provide some numerical examples to illustrate the results and analyze the VaR control levels on the optimal strategy.

A comparison of the Normal and Laplace distributions in the models of fuzzy probability distribution for portfolio selection

The propose of this work is applied the fuzzy Laplace distribution on a possibilistic mean-variance model presented by Li et al which appliehe fuzzy normal distribution. The theorem necessary to introduce the Laplace distribution in the model was demonstrated. It was made an analysis of the behavior of the fuzzy normal and fuzzy Laplace distributions on the portfolio selection with VaR constraint and risk-free investment considering real data. The results showns that were not difference in assets selection and in return rate, however, There was a change in the risk rate, which was higher in the Laplace distribution than in the normal distribution.

Optimal asset allocation for participating contracts under the VaR and PI constraint

ABSTRACTParticipating contracts provide a maturity guarantee for the policyholder. However, the terminal payoff to the policyholder should be related to financial risks of participating insurance contracts. We investigate an optimal investment problem under a joint value-at-risk and portfolio insurance constraint faced by the insurer who offers participating contracts. The insurer aims to maximize the expected utility of the terminal payoff to the insurer. We adopt a concavification technique and a Lagrange dual method to solve the problem and derive the representations of the optimal wealth process and trading strategies. We also carry out some numerical analysis to show how the joint value-at-risk and the portfolio insurance constraint impacts the optimal terminal wealth.

Solution of Hamilton-Jacobi-Bellman Equation in Optimal Reinsurance Strategy under Dynamic VaR Constraint

This paper analyzes the optimal reinsurance strategy for insurers with a generalized mean-variance premium principle. The surplus process of the insurer is described by the diffusion model which is an approximation of the classical Cramér-Lunderberg model. We assume the dynamic VaR constraints for proportional reinsurance. We obtain the closed form expression of the optimal reinsurance strategy and corresponding survival probability under proportional reinsurance.

Optimal investment under VaR-Regulation and Minimum Insurance

We look at an optimal investment problem of a financial institution operating under a joint Value-at-Risk and a portfolio insurance constraint. This analysis is particularly relevant for an insurance company operating under the Solvency II regulation which aims to maximize the expected utility of its shareholders, while at the same time being required to provide its policyholders a minimum guaranteed amount. Using static Lagrangian method, we solve the pointwise utility optimization problem to achieve the global maximum by carefully comparing the local maximizers with the jump point or the boundary. Our theoretical and numerical results show that contrary to a pure Value-at-Risk regulation, an insurance company that operates not only under a Solvency II VaR constraint but additionally has to serve a minimal guarantee admits a comprehensive but not too costly protection, and at the same time displays prudent investment behavior. This result holds for both constant and stochastic volatility settings.

Portfolio selection based on a benchmark process with dynamic value-at-risk constraints

Portfolio selection is an essential issue in finance. It studies how to allocate one’s wealth in a basket of securities to maximize the return and minimize the risk. And dynamic portfolio selection based on a benchmark process is one of the most important types. Different from the existing literature, we impose a dynamic risk control on it. As a matter of fact, performing an optimal portfolio strategy in the light of a dynamic portfolio formulation does not eliminate the possibility of an investor going to bankruptcy or even more serious situations in a volatile financial market before the terminal time, so it is reasonable and necessary to impose a dynamic risk control on the instantaneous wealth throughout the investment horizon to ensure that the investment behavior can proceed and we intend to address this interesting issue in this paper. More specifically, we investigate the dynamic portfolio selection problem based on a benchmark process coupled with a dynamic value-at-risk constraint. By stochastic dynamic programming techniques, we derive the corresponding Hamilton–Jacobi–Bellman equation. Moreover, the optimal portfolio strategies are obtained by Lagrange multiplier method. To verify the model, two numerical examples are illustrated. The results show the difference of optimal portfolio strategies with and without the dynamic VaR constraint: the composition of the risky assets is constant but the investment proportion is reduced as the VaR constraint becomes binding. This research can provide a good decision-making reference for risk-averse investors.

Optimal insurance contract under VaR and CVaR constraints

This study endogenously develops an optimal insurance contractual form for maximizing insured expected utility under VaR and CVaR constraints. We find that CVaR constraint does not affect the contractual form, but may increase minimum insurance premium requirement. Additionally, when the VaR constraint is binding, the optimal contract is a double deductible insurance. However, if the contract is restricted to a regular form (both indemnity schedule and retained loss schedule are continuously nondecreasing) for avoiding moral hazard problem, the optimal contract is a piecewise linear deductible insurance. Finally, we provide intuitive comparison between this study result and relevant studies.

How risk managers should fix tracking error volatility and value-at-risk constraints in asset management

Investors usually assign part of their funds to asset managers, who are given the task of beating a benchmark. managers usually face a constraint on maximum tracking error volatility (TEV), which is imposed by the risk management office. In the mean-variance space, Jorion, in his 2003 paper Portfolio optimization with tracking-error constraints, shows that this constraint determines an ellipse containing all admissible portfolios. However, many admissible portfolios have problems in mean-variance terms, for example, because of an overly high variance. To overcome this problem, Jorion also fixes a constraint on variance, while, in their 2008 paper Active portfolio management with benchmarking: adding a value-at-risk constraint, Alexander and Baptista fix a constraint on value-at-risk (VaR). In this paper, I determine an optimal value for a set of limits composed of the lower limit on TEV, the upper limit on TEV and the upper limit on VaR. To fix the upper limit on VaR, I use the TEV constrained efficient frontier developed in Palomba and Riccetti's 2013 paper Asset management with TEV and VAR constraints: the constrained efficient frontiers, which is the set of portfolios that is on Jorion's ellipse and not dominated from the mean-variance perspective. In particular, I develop a strategy to impose on asset managers a set of portfolios that contains as many TEV constrained efficient portfolios and as few inefficient portfolios as possible. Moreover, I show that a limit on maximum VaR is usually better than a limit on maximum variance.

Portfolio choices and VaR constraint with a defaultable asset

We consider a Constant Elasticity of Variance (CEV) model for the asset price of a defaultable asset showing the so-called leverage effect (high volatility when the asset price is low). We show that a VaR constraint re-evaluated over time induces an agent more risk averse than a logarithmic utility to take more risk than in the unconstrained setting.

Mean-VAR Model with Stochastic Volatility

The objective of this article is the research of optimal portfolio strategy under a probability constraint of type Value-at-Risk in setting of stochastic volatility model. Our decision problem is the optimal combination of risky asset and certain asset by maximizing the utility function under the VaR constraint that is limited by a loss proportional to current return. The empirical results show that the VaR constraint decreases the amount invested in risky asset gradually over time. We also note that volatility has a significant impact on the optimal solution. Furthermore, this approach is more appropriate when the investor sets a confidence level high enough and low holding period. In addition, this model allows us to better understand the form of the distribution and offers the advantage to the investor to take account of asymmetric and leptokurtic distributions of stock market returns.

Asset Management with TEV and VAR Constraints: The Constrained Efficient Frontiers

It is well known that investors usually assign part of their funds to asset managers who are given the task of beating a benchmark portfolio. On the other hand, the risk management office could impose some restrictions to the asset managers' activity in order to maintain the overall portfolio risk under control. This situation could lead managers to select non efficient portfolios in the total return and absolute risk perspective.In this paper we focus on portfolio efficiency when a tracking error volatility (TEV) constraint holds. First, we define the TEV Constrained-Efficient Frontier (ECTF), a set of TEV constrained portfolios that are mean-variance efficient. Second, we discuss the effects on such boundary when a VaR and/or a variance restriction is also added.

Optimal stochastic differential games with VaR constraints

The nonlinear dynamic games between competing insurance companies are interesting and important problemsbecause of the general practice of using re-insurance to reduce risks in the insurance industry. This problem becomes more complicatedif a proper risk control is imposed on all the involving companies. In order to understand the dynamical properties,we consider the stochastic differential game between two insurance companies with risk constraints. The companies are allowed to purchase proportional reinsurance and invest their money into both risk free asset and risky (stock) asset. The competition between the two companies is formulated as a two player (zero-sum) stochastic differential game. One company chooses the optimal reinsurance and investment strategy in order to maximize the expected payoff, and the other one tries to minimize this value. For the purpose of risk management, the risk arising from the whole portfolio is constrained to some level. By the principle of dynamic programming, the problem is reduced to solving the Hamilton-Jacobi-Bellman-Isaacs (HJBI) equations for Nash equilibria. We derive the Nash equilibria explicitly and obtain closed form solutions to HJBI under different scenarios.

When Micro Prudence Increases Macro Risk: The Destabilizing Effects of Financial Innovation, Leverage, and Diversification

By exploiting basic common practice accounting and risk management rules, we propose a simple analytical dynamical model to investigate the effects of micro-prudential changes on macro-prudential outcomes. Specifically, we study the consequence of the introduction of a financial innovation that allow reducing the cost of portfolio diversification in a financial system populated by financial institutions having capital requirements in the form of VaR constraint, and following standard mark-to-market and risk management rules. We provide a full analytical quantification of the multivariate feedback effects between investment prices and bank behavior induced by portfolio re-balancing in presence of asset lliquidity, and show how changes in the constraints of the bank portfolio optimization endogenously drive the dynamics of the balance sheet aggregate of financial institutions and, thereby, the availability of bank liquidity to the economic system and systemic risk. The model shows that when financial innovation reduces the cost of diversification below a given threshold, the strength (due to higher leverage) and coordination (due to similarity of bank portfolios) of feedback effects increase, triggering a transition from a stationary dynamics of price returns to a non stationary one characterized by steep growths (bubbles) and plunges (bursts) of market prices.

Fuzzy possibilistic portfolio selection model with VaR constraint and risk-free investment

We propose a possibilistic portfolio model with VaR constraint and risk-free investment based on the possibilistic mean and variance, while assuming that the expected rate of returns is a fuzzy number. The model shows more clearly that, in the financial market affected by several non-probabilistic factors, risk-averse investors wish not only to reach the expected rate of returns in their actual investment, but also to assure that the maximum of their possible future risk is lower than an expected loss. Under the condition that the expected rate of returns is a normal distribution fuzzy variable, we proposed a theorem as the solution, and derive a crisp equivalent form of the possibilistic portfolio under constraints of VaR and risk-free investment. This model is an expansion of the fuzzy possibilistic mean–variance model by Zhang (2007). Finally, an empirical study is carried out using the data concerning some stocks of various industries listed at the Shanghai Stock Exchange. A conclusion is reached that the investors are able to choose a portfolio more suitable to them under the VaR constraint.

Incentive Contract in Delegated Portfolio Management Under VaR Constraint

Linear contracts are popular in delegated portfolio management. This paper studies the incentive of linear performance-adjusted contracts in delegated portfolio management under a VaR constraint with a principal-agent model and numerical analysis. It is shown that a linear performance-based contract provides incentives to a portfolio manager to work at acquiring private information under a total risk constraint. The expected utility and optimal effort are increasing functions of the return sharing ratio for a risk-averse manager. However, a risk constraint makes a portfolio manager to reduce effort in gathering private information, suggesting that the VaR constraint increases the moral hazard between the investor and the manager.