On Valuation and Investments of Pension Plans in Discrete Incomplete Markets

Michail Anthropelos () and Evmorfia Blontzou
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Michail Anthropelos: Department of Banking & Financial Management, University of Piraeus, 185 34 Pireas, Greece
Evmorfia Blontzou: Department of Banking & Financial Management, University of Piraeus, 185 34 Pireas, Greece

Risks, 2023, vol. 11, issue 6, 1-24

Abstract: We study the valuation of a pension fund’s obligations in a discrete time and space incomplete market model. The market’s incompleteness stems from the non-replicability of the wage process that finances the pension plan through time. The contingent defined-benefit liability of the pension fund is a function of the wages, which can be seen as the payoff of a path-dependent derivative security. We apply the notion of the super-hedging value and propose its difference from the current pension’s fund capital as a measure of distance to liability hedging. The induced closed-form expressions of the values and the related investment strategies provide insightful comparative statistics. Furthermore, we use a utility-based optimization portfolio to point out that in cases of sufficient capital, the application of a subjective investment criterion may result in heavily different strategies than the super-hedging one. This means that the pension fund will be left with some liability risk, although it could have been fully hedged. Finally, we provide conditions under which the effect of a possible early exit leaves the super-hedging valuation unchanged.

Keywords: valuation of pension plans; defined benefit scheme; super-hedging price; utility maximization for pension funds; early exit from pension plan (search for similar items in EconPapers)
JEL-codes: C G0 G1 G2 G3 K2 M2 M4 (search for similar items in EconPapers)
Date: 2023
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