Optimal Pension Insurance Design

Abstract

In this paper we provide a framework for how the traditional life and pension contracts with a guaranteed rate of return can be optimized to increase customers' welfare. Given that the contracts have to be priced correctly, we use individuals' preferences to find the preferred design. Assuming CRRA utility, we cannot explain the existence of any form of guarantees. Through numerical solutions we quantify the difference (measured in security equivalents) to the preferred Merton solution of direct investments in a fixed proportion of risky and risk free assets. The largest welfare loss seems to come from the fact that guarantees are effective by the end of each year, not only by the expiry of the contract. However, the demand for products with guarantees may be explained through behavioral models accounting for loss aversion, e.g. cumulative prospect theory. In this case, the optimal design seems to be a simple contract with a life-time guarantee.

Cumulative prospect theory and mean–variance analysis: a rigorous comparison

“…This notion of a certainty equivalent has been employed for comparative purposes e.g. by Døskeland and Nordahl (2006) [9] and by De Giorgi and Hens (2009) [6].…”

How Good Are Portfolio Insurance Strategies?

“…In consequence, to some extent, guarantees can be explained with respect to the assumption that the investor's preferences can be described using the von Neumann and Morgenstern (1944) framework of expected utility. More recently, Doskeland and Nordahl (2008) justify the existence of guarantees through behavioral models. In particular, they use cumulative prospect theory as an example.…”

“…Amongst early papers on the optimality of portfolio insurance are also Leland (1980) and Benninga and Blume (1985). More recently, Doskeland and Nordahl (2008) justify the existence of guarantees from the point of an investor through behavioral models. In particular, they use cumulative prospect theory as an example.…”

Intergenerational effects of guaranteed pension contracts

“…Intuitively one would think that companies should invest higher proportions in stocks to get closer to the optimal asset allocation for customers (see e.g. Døskeland and Nordahl (2006) for details). However, as companies prefer to satisfy new customers (the later generations) they may prefer a lower θ.…”

“…According to Borch, we cannot explain the existence of these saving vehicles within an one-generation expected utility framework with HARA utility, as these contracts have a non-linear pay-out function. Jensen and Sørensen (2001), Consiglio, Saunders, and Zenios (2006) and Døskeland and Nordahl (2006) build on this point by quantifying the effects in various cases of interest rate guarantees. However, previous research assume that all generations receive the same return.…”