Individual optimal pension allocation under stochastic dominance constraints

Abstract

An individual investor has to decide how to allocate his/her savings from a retirement perspective. This problem covers a long-term horizon. In this paper we consider a 40-year horizon formulating a multi-criteria multistage program with stochastic dominance constraints in an intermediate stage and in the final stage. As we are dealing with a real problem and we have formulated the model in cooperation with a commercial Italian bank, the intermediate stage corresponds to a possible withdrawal allowed by the Italian pension system. The sources of uncertainty considered are: the financial returns, the interest rate evolution, the investor's salary process and a considerable withdrawal event. We include a set of portfolio constraints according to the pension plan regulation. The objective of the model is to minimize the Average Value at Risk Deviation (AV @RD) measure and to satisfy wealth goals. Three different wealth target formulations are considered: a deterministic wealth target (i.e. a comparison between the accumulated average wealth and a fixed threshold) and two stochastic dominance relations -the first order and the second order -introducing a benchmark portfolio and then requiring the optimal portfolio to dominate the benchmark. In particular, we prove that solutions obtained under stochastic dominance constraints ensure a safer allocation while still guaranteeing good returns. Moreover, we show how the withdrawal event affects the solution in terms of allocation in each of the three frameworks. Finally, the sensitivity and convergence of the stochastic solutions and computational issues are investigated.

Assessment of Policy Changes to Means-Tested Age Pension Using Expected Utility Model: Implication for Decisions in Retirement

“…However, the model can benefit from being extended with stochastic dominance theory (Kopa et al 2016;Levy 2006) or prospect theory (Kahneman and Tversky 1979), in order to avoid the inherent limitations of the standard utility theory. This is the subject of future research.…”

“…The key work for early models was laid out by Yaari (1964Yaari ( , 1965, who extended the model with uncertain lifetime and studied the optimal choice of life insurance and annuities, while Samuelson (1969) and Merton (1969Merton ( , 1971) studied the problem in relation to optimal portfolio allocation. Nowadays, there are extended theories available such as prospect theory (Kahneman and Tversky 1979) or stochastic dominance theory (Kopa et al 2016;Levy 2006). While prospect theory is based on the findings that individuals often violate expected utility maximization, the stochastic dominance is developed on the foundation of the expected utility paradigm.…”

A conservative discontinuous target volatility strategy

“…In particular, we verify if there exist some stochastic dominance relations, namely the first order (FSD), second order (SSD) and third order stochastic dominance (TSD) (see Müller and Stoyan, 2002;Davidson and Duclos, 2000;Kopa and Post, 2015;Kopa et al, 2016). e motivation of the following part is due to the fact that in previous analysis, the Sharpe Ratio and the Rachev Ratio did not produce a clear evidence about what an investor should prefer, since the values of the Ratios were very close and the return of the S&P 500 was always higher than the other proposed strategies.…”

ALM models based on second order stochastic dominance

“…The conceptual advantages of using SSD in asset allocation has been long recognised, along with computational difficulties in applying it (Whitmore and Findlay 1978). Recently, computationally tractable optimisation models based on SSD have been proposed for single stage portfolio optimisation-for example, Dentcheva and Ruszczynski (2006), Roman et al (2006), Fábián et al (2011a, b), Post and Kopa (2013), Kopa and Post (2015) and very recently for multistage SP problems-see for example Escudero et al (2016) and Kopa et al (2018).…”