Mean-Variance Investment and Reinsurance Optimization with Stochastic Interest Rate and Volatility
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Informa UK Limited
Abstract
This paper studies a continuous-time investment and reinsurance problem for an insurer. The financial market consists of one money market asset, one stock, and two zero-coupon bonds. Interest rates follow a generalized Cox-Ingersoll-Ross model, and the stock price is given by the Heston stochastic volatility model, with the stochastic interest rate and volatility processes being correlated. The insurer purchases proportional reinsurance to mitigate its risk and invests the surplus in the financial market, with the purpose to optimize mean-variance preferences in the precommitment sense. By the theory of backward stochastic differential equations and linear-quadratic control, the insurer's efficient strategy and efficient frontier are both obtained in closed form. An empirical analysis using market data validates the proposed financial model, and a numerical study offers valuable insights into the impact of model inputs on the insurer's efficient frontier.Description
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3801 Applied Economics, 35 Commerce, Management, Tourism and Services, 38 Economics, 3502 Banking, Finance and Investment, 4901 Applied Mathematics, 4905 Statistics, 49 Mathematical Sciences, 01 Mathematical Sciences, 14 Economics, 15 Commerce, Management, Tourism and Services, Finance, 35 Commerce, management, tourism and services, 38 Economics, 49 Mathematical sciences
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Quantitative Finance, ISSN: 1469-7688 (Print); 1469-7696 (Online), Informa UK Limited, 25(10), 1615-1637. doi: 10.1080/14697688.2025.2566353
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© 2025 The Author(s). Published by Informa UK Limited, trading as Taylor & Francis Group. This is an Open Access article distributed under the terms of the Creative Commons Attribution-NonCommercial-NoDerivatives License (http://creativecommons.org/licenses/by-nc-nd/4.0/), which permits non-commercial re-use, distribution, and reproduction in any medium, provided the original work is properly cited, and is not altered, transformed, or built upon in any way. The terms on which this article has been published allow the posting of the Accepted Manuscript in a repository by the author(s) or with their consent.