Constrained LQ Problem with a Random Jump and Application to Portfolio Selection


Yuchao DONG.Constrained LQ Problem with a Random Jump and Application to Portfolio Selection[J].Chinese Annals of Mathematics B,2018,39(5):829~848
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Yuchao DONG;


This work was supported by the National Natural Science Foundation of China (Nos.10325101, 11171076) and the Shanghai Outstanding Academic Leaders Plan (No.14XD1400400).
Abstract: This paper deals with a constrained stochastic linear-quadratic (LQ for short) optimal control problem where the control is constrained in a closed cone. The state process is governed by a controlled SDE with random coefficients. Moreover, there is a random jump of the state process. In mathematical finance, the random jump often represents the default of a counter party. Thanks to the It\^o-Tanaka formula, optimal control and optimal value can be obtained by solutions of a system of backward stochastic differential equations (BSDEs for short). The solvability of the BSDEs is obtained by solving a recursive system of BSDEs driven by the Brownian motions. The author also applies the result to the mean variance portfolio selection problem in which the stock price can be affected by the default of a counterparty.


Backward stochastic Riccati equation, Default time, Mean-variance problem


60H15, 35R60, 93E20
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