Abstract
This paper studies a continuous-time market under a stochastic environment where an agent, having specified an investment horizon and a target terminal mean return, seeks to minimize the variance of the return with multiple stocks and a bond. In the model considered here, the mean returns of individual assets are explicitly affected by underlying Gaussian economic factors. Using past and present information of the asset prices, a partial-information stochastic optimal control problem with random coefficients is formulated. Here, the partial information is due to the fact that the economic factors can not be directly observed. Using dynamic programming theory, we show that the optimal portfolio strategy can be constructed by solving a deterministic forward Riccati-type ordinary differential equation and two linear deterministic backward ordinary differential equations.
Highlights
Mean-variance is an important investment decision rule in financial portfolio selection, which is first proposed and solved in the single-period setting by Markowitz in his Nobel-Prize-winning works [1] [2]
The variance of the final wealth is used as a measure of the risk associated with the portfolio and the agent seeks to minimize the risk of his investment subject to a given mean return
This model becomes the foundation of modern finance theory and inspires hundreds of extension and applications
Summary
Mean-variance is an important investment decision rule in financial portfolio selection, which is first proposed and solved in the single-period setting by Markowitz in his Nobel-Prize-winning works [1] [2]. The variance of the final wealth is used as a measure of the risk associated with the portfolio and the agent seeks to minimize the risk of his investment subject to a given mean return This model becomes the foundation of modern finance theory and inspires hundreds of extension and applications. (2014) Continuous-Time Mean-Variance Portfolio Selection with Partial Information. This paper attempts to deal with the mean-variance portfolio selection under partial information based on the model of [12]. The mean-variance portfolio selection problem, with respect to the initial wealth x0 , is formulated as a constrained stochastic optimization problem parameterized by x ≥ x0e∫0Tr(t)dt : minimize. We will call problem (2.14) the auxiliary problem of the original problem (2.12)
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