共查询到20条相似文献,搜索用时 31 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.
10.
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
11.
Considering the stochastic exchange rate, a four-factor futures model with the underling asset, convenience yield, instantaneous
risk free interest rate and exchange rate, is established. These processes follow jump-diffusion processes (Weiner process
and Poisson process). The corresponding partial differential equation (PDE) of the futures price is derived. The general solution
of the PDE with parameters is drawn. The weight least squares approach is applied to obtain the parameters of above PDE. Variance
is substituted by semi-variance in Markowitzs portfolio selection model. Therefore, a class of multi-period semi-variance
model is formulated originally. Then, a continuous-time mean-variance portfolio model is also considered. The corresponding
stochastic Hamilton-Jacobi-Bellman (HJB) equation of the problem with nonlinear constraints is derived. A numerical algorithm
is proposed for finding the optimal solution in this paper. Finally, in order to demonstrate the effectiveness of the theoretical
models and numerical methods, the fuel futures in Shanghai exchange market and the Brent crude oil futures in London exchange
market are selected to be examples. 相似文献
12.
We consider the optimal portfolio selection problem in a multiple period setting where the investor maximizes the expected
utility of the terminal wealth in a stochastic market. The utility function has an exponential structure and the market states
change according to a Markov chain. The states of the market describe the prevailing economic, financial, social and other
conditions that affect the deterministic and probabilistic parameters of the model. This includes the distributions of the
random asset returns as well as the utility function. The problem is solved using the dynamic programming approach to obtain
the optimal solution and an explicit characterization of the optimal policy. We also discuss the stochastic structure of the
wealth process under the optimal policy and determine various quantities of interest including its Fourier transform. The
exponential return-risk frontier of the terminal wealth is shown to have a linear form. Special cases of multivariate normal
and exponential returns are disussed together with a numerical illustration. 相似文献
13.
Stochastic optimal control of DC pension funds 总被引:1,自引:0,他引:1
In this paper, we study the portfolio problem of a pension fund manager who wants to maximize the expected utility of the terminal wealth in a complete financial market with the stochastic interest rate. Using the method of stochastic optimal control, we derive a non-linear second-order partial differential equation for the value function. As it is difficult to find a closed form solution, we transform the primary problem into a dual one by applying a Legendre transform and dual theory, and try to find an explicit solution for the optimal investment strategy under the logarithm utility function. Finally, a numerical simulation is presented to characterize the dynamic behavior of the optimal portfolio strategy. 相似文献
14.
We consider a financial market model with a single risky asset whose price process evolves according to a general jump-diffusion with locally bounded coefficients and where market participants have only access to a partial information flow. For any utility function, we prove that the partial information financial market is locally viable, in the sense that the optimal portfolio problem has a solution up to a stopping time, if and only if the (normalised) marginal utility of the terminal wealth generates a partial information equivalent martingale measure (PIEMM). This equivalence result is proved in a constructive way by relying on maximum principles for stochastic control problems under partial information. We then characterize a global notion of market viability in terms of partial information local martingale deflators (PILMDs). We illustrate our results by means of a simple example. 相似文献
15.
Valeri I. Zakamouline 《Mathematical Methods of Operations Research》2005,62(2):319-343
In this paper we study the continuous time optimal portfolio selection problem for an investor with a finite horizon who maximizes
expected utility of terminal wealth and faces transaction costs in the capital market. It is well known that, depending on
a particular structure of transaction costs, such a problem is formulated and solved within either stochastic singular control
or stochastic impulse control framework. In this paper we propose a unified framework, which generalizes the contemporary
approaches and is capable to deal with any problem where transaction costs are a linear/piecewise-linear function of the volume
of trade. We also discuss some methods for solving numerically the problem within our unified framework. 相似文献
16.
Paulwin Graewe Ulrich Horst Eric Séré 《Stochastic Processes and their Applications》2018,128(3):979-1006
We consider the stochastic control problem of a financial trader that needs to unwind a large asset portfolio within a short period of time. The trader can simultaneously submit active orders to a primary market and passive orders to a dark pool. Our framework is flexible enough to allow for price-dependent impact functions describing the trading costs in the primary market and price-dependent adverse selection costs associated with dark pool trading. We prove that the value function can be characterized in terms of the unique smooth solution to a PDE with singular terminal value, establish its explicit asymptotic behavior at the terminal time, and give the optimal trading strategy in feedback form. 相似文献
17.
In this paper, we consider the optimal portfolio selection problem in continuous-time settings where the investor maximizes the expected utility of the terminal wealth in a stochastic market. The utility function has the structure of the HARA family and the market states change according to a Markov process. The states of the market describe the prevailing economic, financial, social and other conditions that affect the deterministic and probabilistic parameters of the model. This includes the distributions of the random asset returns as well as the utility function. We analyzed Black–Scholes type continuous-time models where the market parameters are driven by Markov processes. The Markov process that affects the state of the market is independent of the underlying Brownian motion that drives the stock prices. The problem of maximizing the expected utility of the terminal wealth is investigated and solved by stochastic optimal control methods for exponential, logarithmic and power utility functions. We found explicit solutions for optimal policy and the associated value functions. We also constructed the optimal wealth process explicitly and discussed some of its properties. In particular, it is shown that the optimal policy provides linear frontiers. 相似文献
18.
19.
We consider stochastic control problems with jump-diffusion processes and formulate an algorithm which produces, starting
from a given admissible control π, a new control with a better value. If no improvement is possible, then π is optimal. Such an algorithm is well-known for discrete-time Markov Decision Problems under the name Howard’s policy improvement algorithm. The idea can be traced back to Bellman. Here we show with the help of martingale techniques that such an algorithm can also
be formulated for stochastic control problems with jump-diffusion processes. As an application we derive some interesting
results in financial portfolio optimization. 相似文献
20.
Robert J. Elliott Tak Kuen Siu 《Nonlinear Analysis: Theory, Methods & Applications》2011,74(17):6302-6313
In this paper, we study utility-based indifference pricing and hedging of a contingent claim in a continuous-time, Markov, regime-switching model. The market in this model is incomplete, so there is more than one price kernel. We specify the parametric form of price kernels so that both market risk and economic risk are taken into account. The pricing and hedging problem is formulated as a stochastic optimal control problem and is discussed using the dynamic programming approach. A verification theorem for the Hamilton-Jacobi-Bellman (HJB) solution to the problem is given. An issuer’s price kernel is obtained from a solution of a system of linear programming problems and an optimal hedged portfolio is determined. 相似文献