Equity Allocation and Portfolio Selection in Insurance: A simplified Portfolio Model

TL;DR

This paper introduces a quadratic probabilistic model for optimal insurance portfolio selection, optimizing expected returns while managing risk and return constraints, with proofs of solution existence and methods for solving the model.

Contribution

It presents a novel quadratic discrete-time model for insurance portfolio optimization, including solution existence proofs and an effective approach to solving the associated equations.

Findings

Proved the existence of a unique optimal solution.

Developed an effective method for solving the Euler-Lagrange equations.

Discussed approximate methods for determining multipliers.

Abstract

A quadratic discrete time probabilistic model, for optimal portfolio selection in (re-)insurance is studied. For positive values of underwriting levels, the expected value of the accumulated result is optimized, under constraints on its variance and on annual ROE's. Existence of a unique solution is proved and a Lagrangian formalism is given. An effective method for solving the Euler-Lagrange equations is developed. The approximate determination of the multipliers is discussed. This basic model is an important building block for more complete models.