The Experts below are selected from a list of 21357 Experts worldwide ranked by ideXlab platform
Waiki Ching - One of the best experts on this subject based on the ideXlab platform.
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optimal portfolios with maximum value at Risk Constraint under a hidden markovian regime switching model
Automatica, 2016Co-Authors: Dongmei Zhu, Waiki Ching, Yue Xie, Tak Kuen SiuAbstract: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.
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optimal investment reinsurance with dynamic Risk Constraint and regime switching
Scandinavian Actuarial Journal, 2013Co-Authors: Jingzhen Liu, Ka Cedric Fai Yiu, Tak Kuen Siu, Waiki ChingAbstract:We study an optimal investment–reinsurance problem for an insurer who faces dynamic Risk Constraint in a Markovian regime-switching environment. The goal of the insurer is to maximize the expected utility of terminal wealth. Here the dynamic Risk Constraint is described by the maximal conditional Value at Risk over different economic states. The rationale is to provide a prudent investment–reinsurance strategy by taking into account the worst case scenario over different economic states. Using the dynamic programming approach, we obtain an analytical solution of the problem when the insurance business is modeled by either the classical Cramer–Lundberg model or its diffusion approximation. We document some important qualitative behaviors of the optimal investment–reinsurance strategies and investigate the impacts of switching regimes and Risk Constraint on the optimal strategies.
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optimal portfolios with regime switching and value at Risk Constraint
Automatica, 2010Co-Authors: Waiki ChingAbstract:We consider the optimal portfolio selection problem subject to a maximum value-at-Risk (MVaR) Constraint when the price dynamics of the Risky asset are governed by a Markov-modulated geometric Brownian motion (GBM). Here, the market parameters including the market interest rate of a bank account, the appreciation rate and the volatility of the Risky asset switch over time according to a continuous-time Markov chain, whose states are interpreted as the states of an economy. The MVaR is defined as the maximum value of the VaRs of the portfolio in a short time duration over different states of the chain. We formulate the problem as a constrained utility maximization problem over a finite time horizon. By utilizing the dynamic programming principle, we shall first derive a regime-switching Hamilton-Jacobi-Bellman (HJB) equation and then a system of coupled HJB equations. We shall employ an efficient numerical method to solve the system of coupled HJB equations for the optimal constrained portfolio. We shall provide numerical results for the sensitivity analysis of the optimal portfolio, the optimal consumption and the VaR level with respect to model parameters. These results are also used to investigating the effect of the switching regimes.
Tak Kuen Siu - One of the best experts on this subject based on the ideXlab platform.
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robust reinsurance contracts with Risk Constraint
Scandinavian Actuarial Journal, 2020Co-Authors: Ning Wang, Tak Kuen SiuAbstract:This paper aims to investigate optimal reinsurance contracts in a continuous-time modelling framework from the perspective of a principal-agent problem. The reinsurer plays the role of the principa...
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optimal portfolios with maximum value at Risk Constraint under a hidden markovian regime switching model
Automatica, 2016Co-Authors: Dongmei Zhu, Waiki Ching, Yue Xie, Tak Kuen SiuAbstract: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.
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optimal investment of an insurer with regime switching and Risk Constraint
Scandinavian Actuarial Journal, 2014Co-Authors: Jingzhen Liu, Ka Fai Cedric Yiu, Tak Kuen SiuAbstract:We investigate an optimal investment problem of an insurance company in the presence of Risk Constraint and regime-switching using a game theoretic approach. A dynamic Risk Constraint is considered where we constrain the uncertainty aversion to the ‘true’ model for financial Risk at a given level. We describe the surplus of an insurance company using a general jump process, namely, a Markov-modulated random measure. The insurance company invests the surplus in a Risky financial asset whose dynamics are modeled by a regime-switching geometric Brownian motion. To incorporate model uncertainty, we consider a robust approach, where a family of probability measures is cosidered and the insurance company maximizes the expected utility of terminal wealth in the ‘worst-case’ probability scenario. The optimal investment problem is then formulated as a constrained two-player, zero-sum, stochastic differential game between the insurance company and the market. Different from the other works in the literature, our te...
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optimal investment reinsurance with dynamic Risk Constraint and regime switching
Scandinavian Actuarial Journal, 2013Co-Authors: Jingzhen Liu, Ka Cedric Fai Yiu, Tak Kuen Siu, Waiki ChingAbstract:We study an optimal investment–reinsurance problem for an insurer who faces dynamic Risk Constraint in a Markovian regime-switching environment. The goal of the insurer is to maximize the expected utility of terminal wealth. Here the dynamic Risk Constraint is described by the maximal conditional Value at Risk over different economic states. The rationale is to provide a prudent investment–reinsurance strategy by taking into account the worst case scenario over different economic states. Using the dynamic programming approach, we obtain an analytical solution of the problem when the insurance business is modeled by either the classical Cramer–Lundberg model or its diffusion approximation. We document some important qualitative behaviors of the optimal investment–reinsurance strategies and investigate the impacts of switching regimes and Risk Constraint on the optimal strategies.
Jianjun Gao - One of the best experts on this subject based on the ideXlab platform.
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dynamic mean variance portfolio optimization with value at Risk Constraint in continuous time
Social Science Research Network, 2020Co-Authors: Ke Zhou, Jianjun GaoAbstract:This paper studies the dynamic mean-Risk portfolio optimization problem with variance and Value-at-Risk(VaR) as the Risk measures in recognizing the importance of incorporating different Risk measures in the portfolio management model. Using the martingale approach and combining it with the quantile optimization technique, we provide the solution framework for this problem and show that the optimal terminal wealth may have different patterns under a general market setting. When the market parameters are deterministic, we develop the closed-form solution for this problem. Examples are provided to illustrate the solution procedure of our method and demonstrate the beneft of our dynamic portfolio model comparing with its static counterpart.
Ka Fai Cedric Yiu - One of the best experts on this subject based on the ideXlab platform.
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optimal investment of an insurer with regime switching and Risk Constraint
Scandinavian Actuarial Journal, 2014Co-Authors: Jingzhen Liu, Ka Fai Cedric Yiu, Tak Kuen SiuAbstract:We investigate an optimal investment problem of an insurance company in the presence of Risk Constraint and regime-switching using a game theoretic approach. A dynamic Risk Constraint is considered where we constrain the uncertainty aversion to the ‘true’ model for financial Risk at a given level. We describe the surplus of an insurance company using a general jump process, namely, a Markov-modulated random measure. The insurance company invests the surplus in a Risky financial asset whose dynamics are modeled by a regime-switching geometric Brownian motion. To incorporate model uncertainty, we consider a robust approach, where a family of probability measures is cosidered and the insurance company maximizes the expected utility of terminal wealth in the ‘worst-case’ probability scenario. The optimal investment problem is then formulated as a constrained two-player, zero-sum, stochastic differential game between the insurance company and the market. Different from the other works in the literature, our te...
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optimal inventory policy with fixed and proportional transaction costs under a Risk Constraint
Mathematical and Computer Modelling, 2013Co-Authors: S Y Wang, Ka Fai Cedric Yiu, Kai Ling MakAbstract:Abstract The traditional inventory models focus on characterizing replenishment policies in order to maximize the total expected profit or to minimize the expected total cost over a planned horizon. However, for many companies, total inventory costs could be accounting for a fairly large amount of invested capital. In particular, raw material inventories should be viewed as a type of invested asset for a manufacturer with suitable Risk control. This paper is intended to provide this perspective on inventory management that treats inventory problems within a wider context of financial Risk management. In view of this, the optimal inventory problem under a VaR Constraint is studied. The financial portfolio theory has been used to model the dynamics of inventories. A diverse portfolio consists of raw material inventories, which involve market Risk because of price fluctuations as well as a Risk-free bank account. The value-at-Risk measure is applied thereto to control the inventory portfolio’s Risk. The objective function is to maximize the utility of total portfolio value. In this model, the ordering cost is assumed to be fixed and the selling cost is proportional to the value. The inventory control problem is thus formulated as a continuous stochastic optimal control problem with fixed and proportional transaction costs under a continuous value-at-Risk (VaR) Constraint. The optimal inventory policies are derived by using stochastic optimal control theory and the optimal inventory level is reviewed and adjusted continuously. A numerical algorithm is proposed and the results illustrate how the raw material price, inventory level and VaR Constraint are interrelated.
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optimal investment and proportional reinsurance with Risk Constraint
Journal of Mathematical Finance, 2013Co-Authors: Jingzhen Liu, Ka Fai Cedric Yiu, Ryan Loxton, Kok Lay TeoAbstract:In this paper, we investigate the problem of maximizing the expected exponential utility for an insurer. In the problem setting, the insurer can invest his/her wealth into the market and he/she can also purchase the proportional reinsurance. To control the Risk exposure, we impose a value-at-Risk Constraint on the portfolio, which results in a constrained stochastic optimal control problem. It is difficult to solve a constrained stochastic optimal control problem by using traditional dynamic programming or Martingale approach. However, for the frequently used exponential utility function, we show that the problem can be simplified significantly using a decomposition approach. The problem is reduced to a deterministic constrained optimal control problem, and then to a finite dimensional optimization problem. To show the effectiveness of the approach proposed, we consider both complete and incomplete markets; the latter arises when the number of Risky assets are fewer than the dimension of uncertainty. We also conduct numerical experiments to demonstrate the effect of the Risk Constraint on the optimal strategy.
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optimal investment with a value at Risk Constraint
Journal of Industrial and Management Optimization, 2012Co-Authors: Jingzhen Liu, Lihua Bai, Ka Fai Cedric YiuAbstract:We consider constrained investment problem with the objective of minimizing the ruin probability. In this paper, we formulate the cash reserve and investment model for the insurance company and analyze the value-at-Risk ($VaR$) in a short time horizon. For Risk regulation, we impose it as a Risk Constraint dynamically. Then the problem becomes minimizing the probability of ruin together with the imposed Risk Constraint. By solving the corresponding Hamilton-Jacobi-Bellman equations, we derive analytic expressions for the optimal value function and the corresponding optimal strategies. Looking at the value-at-Risk alone, we show that it is possible to reduce the overall Risk by an increased exposure to the Risky asset. This is aligned with the Risk diversification effect for negative correlated or uncorrelated Risky asset with the stochastic of the fundamental insurance business. Moreover, studying the optimal strategies, we find that a different investment strategy will be in place depending on the Sharpe ratio of the Risky asset.
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optimal portfolios with stress analysis and the effect of a cvar Constraint
Pacific Journal of Optimization, 2011Co-Authors: J Z Liu, Ka Fai Cedric Yiu, Kok Lay TeoAbstract:Risk-constrained allocation of Risky assets in financial portfolios is particularly important in situations when asset returns appear to have large fluctuations. This problem is addressed here. The asset price is assumed to be driven by a Brownian motion perturbed by a compound Poisson process. This resembles a price process perturbed by an exogenous factor which may cause large movements in price. The jump size of the Poisson process and the rate of jump define, respectively, a scenario and its occurrence probability. The stress testing is conducted to evaluate the performance and assess the resilience of the portfolio subject to exceptional but major events. We examine how a conditional-value- at-Risk Constraint exerts an influence on the portfolio composition.
Alexandre M Baptista - One of the best experts on this subject based on the ideXlab platform.
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active portfolio management with benchmarking adding a value at Risk Constraint
Journal of Economic Dynamics and Control, 2008Co-Authors: Gordon J Alexander, Alexandre M BaptistaAbstract:We examine the impact of adding a value-at-Risk (VaR) Constraint to the problem of an active manager who seeks to outperform a benchmark while minimizing tracking error variance (TEV) by using the model of Roll [1992. A mean/variance analysis of tracking error. Journal of Portfolio Management 18, 13-22]. We obtain three main results. First, portfolios on the constrained mean-TEV boundary still exhibit three-fund separation, but the weights of the three funds when the Constraint binds differ from those in Roll's model. Second, the Constraint mitigates the problem that when an active manager seeks to outperform a benchmark using the mean-TEV model, he or she selects an inefficient portfolio. Finally, when short sales are disallowed, the extent to which the Constraint reduces the optimal portfolio's efficiency loss can still be notable but is smaller than when short sales are allowed.
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active portfolio management with benchmarking adding a value at Risk Constraint
Social Science Research Network, 2007Co-Authors: Gordon J Alexander, Alexandre M BaptistaAbstract:We examine the impact of adding a Value-at-Risk (VaR) Constraint to the problem of an active manager who seeks to outperform a benchmark while minimizing tracking error variance (TEV) by using the model of Roll (1992). We obtain three main results. First, portfolios on the constrained mean-TEV boundary still exhibit three-fund separation, but the weights of the three funds when the Constraint binds differ from those in Roll's model. Second, the Constraint mitigates the problem that when an active manager seeks to outperform a benchmark using the mean-TEV model, he or she selects an inefficient portfolio. Finally, when short sales are disallowed, the extent to which the Constraint reduces the optimal portfolio's efficiency loss can still be notable but is smaller than when short sales are allowed.
