A Quadratic Programming Model of the Non-Life Insurer

Abstract

The purpose of this paper is to provide insurers with a flexible construct which can be of assistance in reaching ex ante portfolio mix decisions. Portfolio theory frequently has been applied to risky asset opportunity sets; however, little attention has been focused on risky asset and risky liability opportunity sets in combination. The insurer attempts to allocate premrums and financial assets to generate positive returns. The study's purpose is to specify optimal ex ante (via ex post) portfolios of underwriting and investment alternatives. These areas are specifically related by applying portfolio theory. The sensitivity of the insurer efficient frontier to alternative constraint definitions is evaluated. Underwriting and asset mix are analyzed as relevant institutional constraints are changed. Considerable controversy has developed in the insurance literature as to the measurement of profitability in the property-liability insurance industry. Clearly the profitability of the industry depends on how effectively the underwriting and investment activities are combined. The degree of industry regulation in its pricing of insurance is controlled by state insurance codes. The insurer insists that these regulated prices include a fair for providing insurance. The regulatory apparatus has seen fit to allow reasonable in the development of sale structures. However, investment returns have not been considered relevant in determining the insurance rate structure until recently. Despite the movement toward including investment income in p-l ratemaking, little agreement exists as to the correct approach for its implementation.' When one makes an attempt to calculate the return and risks to the industry both underwriting and investment functions must be explicitly considered simultaneously. John L. Markle, Ph.D., is a member of the sales staff of Salomon Brothers in New York City. Alfred E. Hofflander, Ph.D., CPCU, CLU, is Professor and Director of Graduate Studies in the Graduate School of Management, University of California, Los Angeles. He is current president of ARIA and an Assistant Editor of the Journal of Risk and Insurance. This paper was accepted for publication in June 1975. 1A recent contribution to this field which attempts to derive an objective analysis of the rationale and feasibility of including investment return in the property-liability ratemaking process is In vestnent Return and Property-Liability Insurance Ratemaking by Robert W. Cooper.