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Open AccessArticle

A Risk-Based Approach for Asset Allocation with A Defaultable Share

by Yang Shen 1,* and Tak Kuen Siu 2
1
Department of Mathematics and Statistics, York University, Toronto, ON M3J 1P3, Canada
2
Department of Applied Finance and Actuarial Studies, Faculty of Business and Economics, Macquarie University, Sydney, NSW 2109, Australia
*
Author to whom correspondence should be addressed.
Risks 2018, 6(1), 14; https://doi.org/10.3390/risks6010014
Received: 15 December 2017 / Revised: 15 February 2018 / Accepted: 17 February 2018 / Published: 27 February 2018
This paper presents a novel risk-based approach for an optimal asset allocation problem with default risk, where a money market account, an ordinary share and a defaultable security are investment opportunities in a general non-Markovian economy incorporating random market parameters. The objective of an investor is to select an optimal mix of these securities such that a risk metric of an investment portfolio is minimized. By adopting a sub-additive convex risk measure, which takes into account interest rate risk, as a measure for risk, the investment problem is discussed mathematically in a form of a two-player, zero-sum, stochastic differential game between the investor and the market. A backward stochastic differential equation approach is used to provide a flexible and theoretically sound way to solve the game problem. Closed-form expressions for the optimal strategies of the investor and the market are obtained when the penalty function is a quadratic function and when the risk measure is a sub-additive coherent risk measure. An important case of the general non-Markovian model, namely the self-exciting threshold diffusion model with time delay, is considered. Numerical examples based on simulations for the self-exciting threshold diffusion model with and without time delay are provided to illustrate how the proposed model can be applied in this important case. The proposed model can be implemented using Excel spreadsheets. View Full-Text
Keywords: asset allocation; sub-additive convex risk measure; default risk; self-exciting threshold diffusion model; time delay asset allocation; sub-additive convex risk measure; default risk; self-exciting threshold diffusion model; time delay
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Shen, Y.; Siu, T.K. A Risk-Based Approach for Asset Allocation with A Defaultable Share. Risks 2018, 6, 14.

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