A kind of time-inconsistent corporate international investment problem with discontinuous cash flow

In this paper, we study a kind of time-inconsistent corporate international investment problem with discontinuous cash flow in consideration of the exchange risk, information costs and taxes. The time-inconsistency arises from the presence of investment risk in the cost functional. We first define the time-consistent equilibrium strategy for this problem and establish a sufficient condition for it through a flow of forward-backward stochastic differential equations with random jumps. When all market parameters are deterministic, an equilibrium strategy is given explicitly by solutions of several ordinary differential equations. Moreover, we present some numerical examples to discuss the influence of market parameters on the equilibrium strategy. It is confirmed that the information costs provide a useful explanation for home bias puzzle in international finance by our time-inconsistent model.

Keywords

corporate international investment, information costs, time-inconsistency, equilibrium strategy, forward-backward stochastic differential equations, ordinary differential equations

2010 Mathematics Subject Classification

91G80, 93E20

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H.W. acknowledges the financial support from the Natural Science Foundation of China (1190 1362) and would like to thank Dr. Yu Fu and Dr. Yuanzhuo Song for their very helpful discussion and comments.

Z.W. acknowledges the financial support from the Natural Science Foundation of China (11831010, 61961160732), the Taishan Scholars Climbing Program of Shandong (TSPD20210302) and the Natural Science Foundation of Shandong Province (ZR2019ZD42).

Received 8 March 2022

Received revised 25 November 2022

Accepted 30 December 2022

Published 9 October 2023