The purpose of this paper is to solve the optimal dynamic portfolio problem under the double-exponential jump diffusion (DEJD) distribution, which can allow the asset returns to jump asymmetrically.
The authors solve the problem by solving the HJB equation. Meanwhile, in the presence of jump component in the asset returns, the investor may suffer a large loss due to high leveraged position, so the authors impose the short-sale and borrowing constraints when solving the optimization problem.
The authors provide sufficient conditions such that the optimal solution exists and show theoretically that the optimal risky asset weight is an increasing function of jump-up probability and average jump-up size and a decreasing function of average jump-down size.
In this study, the authors assume that the jump-up and jump-down intensities are constant. In the future, the authors will relax the assumption and allows the jump intensities to be time varying.
Empirical studies based on Chinese Shanghai stock index data show that the jump distribution of Shanghai index returns is asymmetric, and the DEJD model can fit the data better than the log-normal jump-diffusion model. The numerical results are consistent with the theoretical prediction, and the authors find that the less risk-averse investor will suffer more economic cost if ignoring asymmetric jump distribution.
This study first examines how asymmetric jumps affect the investor’s portfolio allocation.
The authors thank the anonymous referee for their helpful comments. This work is supported by National Natural Science Foundation of China (Nos 71771144, 71320107002).
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