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Optimal Stopping Problems for Asset Management

Part of: Markov processes Stochastic processes

Published online by Cambridge University Press:  04 January 2016

Savas Dayanik  and
Masahiko Egami
Savas Dayanik*
Affiliation:
Bilkent University
Masahiko Egami*
Affiliation:
Kyoto University
*
∗ Postal address: Departments of Industrial Engineering and Mathematics, Bilkent University, 06800 Bilkent, Ankara, Turkey. Email address: sdayanik@bilkent.edu.tr
∗∗ Postal address: Graduate School of Economics, Kyoto University, Yoshida-Honmachi, Sakyo-ku, Kyoto 606-8501, Japan. Email address: egami@econ.kyoto-u.ac.jp
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Abstract

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An asset manager invests the savings of some investors in a portfolio of defaultable bonds. The manager pays the investors coupons at a constant rate and receives a management fee proportional to the value of the portfolio. He/she also has the right to walk out of the contract at any time with the net terminal value of the portfolio after payment of the investors' initial funds, and is not responsible for any deficit. To control the principal losses, investors may buy from the manager a limited protection which terminates the agreement as soon as the value of the portfolio drops below a predetermined threshold. We assume that the value of the portfolio is a jump diffusion process and find an optimal termination rule of the manager with and without protection. We also derive the indifference price of a limited protection. We illustrate the solution method on a numerical example. The motivation comes from the collateralized debt obligations.

Keywords

Optimal stoppingjump diffusionasset management

MSC classification

Primary: 60G40: Stopping times; optimal stopping problems; gambling theory
Secondary: 60J60: Diffusion processes 60J70: Applications of Brownian motions and diffusion theory (population genetics, absorption problems, etc.) 60J75: Jump processes
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 44 , Issue 3 , September 2012 , pp. 655 - 677
Copyright
© Applied Probability Trust 

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