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8:00 hrs. EDT | 6:00 hrs. México
Abstract
This webinar we study the optimal investment-reinsurance problem in the context of equity-linked insurance products. Such products often have a capital guarantee, which can motivate insurers to purchase reinsurance. Since a reinsurance contract implies an interaction between the insurer and the reinsurer, we model the optimization problem as a Stackelberg game. The reinsurer is the leader in the game and maximizes its expected utility by selecting its optimal investment strategy and a safety loading in the reinsurance contract it offers to the insurer. The reinsurer can assess how the insurer will rationally react on each action of the reinsurer. The insurance company is the follower and maximizes its expected utility by choosing its investment strategy and the amount of reinsurance the company purchases at the price offered by the reinsurer. In this game, we derive the Stackelberg equilibrium for general utility functions. For power utility functions, we calculate the equilibrium explicitly and find that the reinsurer selects the largest reinsurance premium such that the insurer may still buy the maximal amount of reinsurance. Since in the equilibrium the insurer is indifferent in the amount of reinsurance, in practice, the reinsurer should consider charging a smaller reinsurance premium than the equilibrium one. Therefore, we propose several criteria for choosing such a discount rate and investigate its wealth-equivalent impact on the expected utility of each party.
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Speaker
Yevhen Havrylenko | Speaker
Yevhen is an applied mathematician with a research focus on data science and decision-making theory with applications to finance and insurance, e.g., equity-linked insurance, asset-liability management with sustainability targets, etc. He has gained practical experience in Asset-Liability Management at Munich Re Group, in Actuarial Pricing at ERGO Group, and in Credit Risk Modeling at two German banks. Yevhen has obtained a doctoral degree from the Technical University of Munich and currently works at the University of Copenhagen, Department of Mathematical Sciences, Section for Insurance and Economics. In his free time, Yevhen enjoys hiking and reading about financial markets.
Pedro Pacheco | Vice Chair IAALS Section
Mexican Actuary currently IAALS Vice Chair, member of the Strategic Planning Committee and Vice Chair of the Health Section (IAAHS), former President of CONAC (México´s FMA in the IAA), President of PREVEM Insurance, with 34 years of experience in the Insurance market on Life and Health. Has been Life and Health Director in MAPFRE Tepeyac 1986-1997, CEO of Zurich Life México from 1997-2004, CEO of AIG Life México from 2004.2009 and currently since 2010 CEO and cofounder of Prevem Seguros (A&H Company).
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