An Extension of Arrow's Result on Optimal Reinsurance Contract

Abstract

We consider the problem of finding reinsurance policies that maximize the expected utility, the stability and the survival probability of the cedent for a fixed reinsurance premium calculated according to the maximal possible claims principle. We show that the limited stop loss and the truncated stop loss are the optimal contracts. Copyright (c) The Journal of Risk and Insurance, 2008.

Robust and Pareto Optimality of Insurance Contracts

“…The seminal papers of Borch (1960) and Arrow (1963) had opened this field of research and since then, many papers discussed this problem under various assumptions on the risk preferences of the insurance players involved in the contract and how the cost of insurance (known as premium ) is quantified. Specifically, the optimal contracts in the context of Expected Utility Theory are investigated amongst others in Kaluszka (2005) , Kaluszka and Okolewski (2008) and Cai and Wei (2012) . Extensive research has been made when the preferences are made via coherent risk measures (as defined in Artzner, Delbaen, Eber, and Heath, 1999 ; recall that CVaR is an element of this class) and VaR; for example, see Cai and Tan (2007) , Balbás, Balbás, and Heras (2009) ; * Corresponding author.…”

Are quantile risk measures suitable for risk-transfer decisions?

“…This holds not just when the reinsurance premium is computed by the expected value principle but also when it is either a continuous function of the m first moments or it a risk-adjusted premium calculation principle as defined by Wang (1996). In particular when the optimization criterion is the VaR we are led to the truncated stop loss, which has already appeared in the actuarial literature when the criterion chosen is the survival probability in one period of time, namely in Gajek and Zagrodny (2004), Kaluszka (2005) and Kaluszka and Okolewski (2008).…”

Optimal reinsurance under adjustment coefficient measure in a discrete risk model based on Poisson MA(1) process

“…Cai & Tan (2007), Cai et al (2008) and Tan et al (2011) present two optimal reinsurance models by minimizing the value at risk and the conditional value at risk of the insurer's total risk exposure. Kaluszka & Okolewski (2008) demonstrate that the limited stop-loss and the truncated stop-loss are the optimal treaties under some criteria including the maximization of the expected utility, the stability, and the survival probability of the cedent.…”