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CPDO WITH FINITE TERMINATION: MAXIMAL RETURN UNDER CASH-IN AND CASH-OUT CONDITIONS

Part of: Mathematical finance Hamilton-Jacobi theories, including dynamic programming Partial differential equations, boundary value problems

Published online by Cambridge University Press:  10 February 2016

X. YANG ,
J. LIANG  and
Y. WU
X. YANG
Affiliation:
Department of Mathematics, Tongji University, Shanghai 200092, PR China email [email protected], [email protected], [email protected]
J. LIANG*
Affiliation:
Department of Mathematics, Tongji University, Shanghai 200092, PR China email [email protected], [email protected], [email protected]
Y. WU
Affiliation:
Department of Mathematics, Tongji University, Shanghai 200092, PR China email [email protected], [email protected], [email protected]
*
✉[email protected]
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Abstract

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The maximal return and optimal leverage of a constant proportion debt obligation with finite termination and two boundaries are analysed by numerically solving Hamilton–Jacobi–Bellman equations. We discuss the probabilities of the asset value reaching the upper or lower bound under the optimal control and the optimal control problem with a time-varying boundary. Furthermore, we also analyse the relationship between the optimal return, the optimal policy and different parameters.

Keywords

CPDOHJB equationcash-incash-outoptimal leverage

MSC classification

Primary: 91G80: Financial applications of other theories (stochastic control, calculus of variations, PDE, SPDE, dynamical systems)
Secondary: 49L20: Dynamic programming method 65N06: Finite difference methods
Type
Research Article
Information
The ANZIAM Journal , Volume 57 , Issue 3 , January 2016 , pp. 207 - 221
Copyright
© 2016 Australian Mathematical Society 

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