共查询到10条相似文献,搜索用时 125 毫秒
1.
Xiang Lin Chunhong Zhang Tak Kuen Siu 《Mathematical Methods of Operations Research》2012,75(1):83-100
We discuss an optimal portfolio selection problem of an insurer who faces model uncertainty in a jump-diffusion risk model
using a game theoretic approach. In particular, the optimal portfolio selection problem is formulated as a two-person, zero-sum,
stochastic differential game between the insurer and the market. There are two leader-follower games embedded in the game
problem: (i) The insurer is the leader of the game and aims to select an optimal portfolio strategy by maximizing the expected
utility of the terminal surplus in the “worst-case” scenario; (ii) The market acts as the leader of the game and aims to choose
an optimal probability scenario to minimize the maximal expected utility of the terminal surplus. Using techniques of stochastic
linear-quadratic control, we obtain closed-form solutions to the game problems in both the jump-diffusion risk process and
its diffusion approximation for the case of an exponential utility. 相似文献
2.
This paper is concerned with a continuous-time mean-variance portfolio selection model that is formulated as a bicriteria
optimization problem. The objective is to maximize the expected terminal return and minimize the variance of the terminal
wealth. By putting weights on the two criteria one obtains a single objective stochastic control problem which is however
not in the standard form due to the variance term involved. It is shown that this nonstandard problem can be ``embedded'
into a class of auxiliary stochastic linear-quadratic (LQ) problems. The stochastic LQ control model proves to be an appropriate
and effective framework to study the mean-variance problem in light of the recent development on general stochastic LQ problems
with indefinite control weighting matrices. This gives rise to the efficient frontier in a closed form for the original portfolio
selection problem.
Accepted 24 November 1999 相似文献
3.
讨论了由金融市场中投资组合和消费选择问题引出的一类最优控制问题,投资者的期望效用是常数相对风险厌恶(CRRA)情形.在跳扩散框架下,利用古典变分法得到了一个局部随机最大值原理.结果应用到最优投资组合和消费选择策略问题,得到了状态反馈形式的显式最优解. 相似文献
4.
This paper establishes a necessary and sufficient stochastic maximum principle for a mean-field model with randomness described by Brownian motions and Poisson jumps. We also prove the existence and uniqueness of the solution to a jump-diffusion mean-field backward stochastic differential equation. A new version of the sufficient stochastic maximum principle, which only requires the terminal cost is convex in an expected sense, is applied to solve a bicriteria mean–variance portfolio selection problem. 相似文献
5.
Amogh Deshpande 《随机分析与应用》2013,31(6):911-933
The finite state semi-Markov process is a generalization over the Markov chain in which the sojourn time distribution is any general distribution. In this article, we provide a sufficient stochastic maximum principle for the optimal control of a semi-Markov modulated jump-diffusion process in which the drift, diffusion, and the jump kernel of the jump-diffusion process is modulated by a semi-Markov process. We also connect the sufficient stochastic maximum principle with the dynamic programming equation. We apply our results to finite horizon risk-sensitive control portfolio optimization problem and to a quadratic loss minimization problem. 相似文献
6.
This paper presents a method for solving multiperiod investment models with downside risk control characterized by the portfolio’s worst outcome. The stochastic programming problem is decomposed into two subproblems: a nonlinear optimization model identifying the optimal terminal wealth distribution and a stochastic linear programming model replicating the identified optimal portfolio wealth. The replicating portfolio coincides with the optimal solution to the investor’s problem if the market is frictionless. The multiperiod stochastic linear programming model tests for the absence of arbitrage opportunities and its dual feasible solutions generate all risk neutral probability measures. When there are constraints such as liquidity or position requirements, the method yields approximate portfolio policies by minimizing the initial cost of the replication portfolio. A numerical example illustrates the difference between the replicating result and the optimal unconstrained portfolio. 相似文献
7.
An incomplete financial market is considered with a risky asset and a bond. The risky asset price is a pure jump process whose dynamics depends on a jump-diffusion stochastic factor describing the activity of other markets, macroeconomics factors or microstructure rules that drive the market. With a stochastic control approach, maximization of the expected utility of terminal wealth is discussed for utility functions of constant relative risk aversion type. Under suitable assumptions, closed form solutions for the value functions and for the optimal strategy are provided and verification results are discussed. Moreover, the solution to the dual problems associated with the utility maximization problems is derived. 相似文献
8.
Consider an insurer who invests in the financial market where correlations among risky asset returns are randomly changing over time. The insurer who faces the risk of paying stochastic insurance claims needs to manage her asset and liability by taking into account of the correlation risk. This paper investigates the impact of correlation risk to the optimal asset–liability management (ALM) of an insurer. We employ the Wishart process to model the stochastic covariance matrix of risky asset returns. The insurer aims to minimize the variance of the terminal wealth given an expected terminal wealth subject to the risk of paying out random liabilities of compound Poisson process. This ALM problem then becomes a linear–quadratic stochastic optimal control problem with stochastic volatilities, stochastic correlations and jumps. The recognition of an affine form in the solution process enables us to derive the explicit closed-form solution to the optimal ALM portfolio policy, obtain the efficient frontier, and identify the condition that the solution is well behaved. 相似文献
9.
Darya Filatova Marek Grzywaczewski Nikolay Osmolovskii 《Nonlinear Analysis: Theory, Methods & Applications》2010,72(3-4):1235-1246
We consider a nonlinear optimal control problem with an integral equation as the control object, subject to control constraints. This integral equation corresponds to the fractional moment of a stochastic process involving short-range and long-range dependences. For both cases, we derive the first-order necessary optimality conditions in the form of the Euler–Lagrange equation, and then apply them to obtain a numerical solution of the problem of optimal portfolio selection. 相似文献