Robust portfolio decisions for financial institutions

Ioannis Baltas; Anastasios Xepapadeas; Athanasios N. Yannacopoulos

doi:10.3934/jdg.2018006

Article Contents

2018, Volume 5, Issue 2: 61-94. Doi: 10.3934/jdg.2018006

This issue Previous Article Next Article Games with nested constraints given by a level structure

Robust portfolio decisions for financial institutions

1.
Department of Financial and Management Engineering, University of the Aegean, 41 Kountouriotou Street, GR-82100, Chios, Greece
2.
Department of International and European Economic Studies, Athens University of Economics and Business, 76 Patission Street, GR-10434, Athens, Greece
3.
Department of Statistics & Laboratory of Stochastic Modeling and Applications, Athens University of Economics and Business, 76 Patission Street, GR-10434, Athens, Greece

Received: September 2017

Revised: December 2017

Published: March 2018

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Abstract

The present paper aims to study a robust-entropic optimal control problem arising in the management of financial institutions. More precisely, we consider an economic agent who manages the portfolio of a financial firm. The manager has the possibility to invest part of the firm's wealth in a classical Black-Scholes type financial market, and also, as the firm is exposed to a stochastic cash flow of liabilities, to proportionally transfer part of its liabilities to a third party as a means of reducing risk. However, model uncertainty aspects are introduced as the manager does not fully trust the model she faces, hence she decides to make her decision robust. By employing robust control and dynamic programming techniques, we provide closed form solutions for the cases of the (ⅰ) logarithmic; (ⅱ) exponential and (ⅲ) power utility functions. Moreover, we provide a detailed study of the limiting behavior, of the associated stochastic differential game at hand, which, in a special case, leads to break down of the solution of the resulting Hamilton-Jacobi-Bellman-Isaacs equation. Finally, we present a detailed numerical study that elucidates the effect of robustness on the optimal decisions of both players.

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Mathematics Subject Classification: Primary: 91A80, 91G10; Secondary: 91A05, 91A25, 93E20.

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Figure 1. Average of 6000 optimal investment strategy paths for various levels of the preference for the robustness parameter, in the case of the exponential utility function.

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Figure 3. Average of 6000 optimal coverage strategy paths for various levels for the preference for the robustness parameter, in the case of the exponential utility function.

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Figure 2. Average of 6000 optimal investment strategy paths for various levels of the initial wealth, in the case of the exponential utility function, with robustness.

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Figure 4. Average of 6000 optimal worst-case strategy paths for various levels for the preference for the robustness parameter, in the case of the exponential utility function.

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