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| Constrained LQ Problem with a Random Jump and Application to Portfolio Selection |
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Citation： |
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 |
| Page view： 1625
Net amount： 1361 |
Authors： |
Yuchao DONG; |
Foundation： |
This work was supported by the National Natural Science
Foundation of China (Nos.10325101, 11171076) and the Shanghai
Outstanding Academic Leaders Plan (No.14XD1400400). |
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| 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. |
Keywords： |
Backward stochastic Riccati equation, Default time, Mean-variance problem |
Classification： |
60H15, 35R60, 93E20 |
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