ALM for insurers with multiple underwriting lines and portfolio constraints: a Lagrangian duality approach

TL;DR

This paper develops a Lagrangian duality framework for optimal asset-liability management in insurance firms with multiple correlated risks, providing explicit strategies and analyzing the effects of risk aversion and constraints.

Contribution

It introduces a novel duality-based approach to optimize investment and underwriting strategies in multi-line insurance portfolios with complex dependencies.

Findings

Explicit optimal strategies under CRRA preferences.

Impact of risk aversion and constraints on earnings retention.

Illustration of co-integration effects in multi-risk scenarios.

Abstract

We study a continuous-time asset-allocation problem for an insurance firm that backs up liabilities from multiple non-life business lines with underwriting profits and investment income. The insurance risks are captured via a multidimensional jump-diffusion process with a multivariate compound Poisson process with dependent components, which allows to model claims that occur in different lines simultaneously. Using Lagrangian convex duality techniques, we provide a general verification-type result for investment-underwriting strategies that maximize expected utility from the dividend payout rate and final wealth over a finite-time horizon. We also study the precautionary effect on earnings retention of risk aversion, prudence, portfolio constraints and multivariate insurance risk. We find an explicit characterization of optimal strategies under CRRA preferences. Numerical results for two-dimensional examples with policy limits illustrate the impact of co-integration for ALM with multiple (dependent and independent) sources of insurance risk.