Abstract
The risk-sensitive asset management problem with a finite horizon is studied under a financial market model having a Wishart autoregressive stochastic factor, which is positive-definite symmetric matrix-valued. This financial market model has the following interesting features: 1) it describes the stochasticity of the market covariance structure, interest rates, and the risk premium of the risky assets; and 2) it admits the explicit representations of the solution to the risk-sensitive asset management problem.
Highlights
Consider a continuous-time financial market that consists of one riskless asset and n risky assets
Example 2.2 (Stochastic Covariance and Interest Rate) We present a slight generalization of Example 2.1 to include stochasticity of interest rates
Under the financial market model comprising (2.1) and (2.2) with the assumptions (2.3) and (2.4), we are interested in treating the risk-sensitive asset management problem (1.3)
Summary
Consider a continuous-time financial market that consists of one riskless asset and n risky assets. T denotes the transpose of a vector or matrix, are semimartingales defined on a filtered probability space tXh e ,f :o l,lo Xw, t i ngtt 0st t0oocfh. I t ment strategy of the investor. Which we call the risk-sensitive asset management problem. AT is a space of admissible investment strategies and is a subset of L2n,T , the totality of n -dimensional t -progressively measurable processes pt t 0,T on the time interval 0,T such that. We reformulate (1.3) with (1.1), (1.2), (1.4), and (1.5) as a linear exponential quadratic Gaussian stochastic control problem, and the optimal investment strategy (portfolio). 2 as 0, where denotes variance, we interpret (1.3) as a risk-sensitized optimization of the expected growth rate maximization, sup GT
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