Optimal investment and reinsurance under exponential forward preferences
Abstract
We study the optimal investment and proportional reinsurance problem of an insurance company, whose investment preferences are described via a forward dynamic utility of exponential type in a stochastic factor model allowing for a possible dependence between the financial and insurance markets. Specifically, we assume that the asset price process dynamics and the claim arrival intensity are both affected by a common stochastic process and we account for a possible environmental contagion effect through the non-zero correlation parameter between the underlying Brownian motions driving the asset price process and the stochastic factor dynamics. By stochastic control techniques, we construct a forward dynamic exponential utility, and we characterize the optimal investment and reinsurance strategy. Moreover, we investigate in detail the zero-volatility case and provide a comparison analysis with classical results in an analogous setting under backward utility preferences. We also discuss an extension of the conditional certainty equivalent. Finally, we perform a numerical analysis to highlight some features of the optimal strategy.
- Publication:
-
arXiv e-prints
- Pub Date:
- October 2022
- DOI:
- 10.48550/arXiv.2210.10425
- arXiv:
- arXiv:2210.10425
- Bibcode:
- 2022arXiv221010425C
- Keywords:
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- Quantitative Finance - Mathematical Finance;
- Quantitative Finance - Portfolio Management;
- 60G55;
- 60J60;
- 91B30;
- 93E20
- E-Print:
- 38 pages, 9 figures