City Research Online

Abstract

This thesis investigates the stability of retirement-income streams and develops optimal investment strategies for collective pension portfolios. First, it scrutinises traditional return-smoothing mechanisms (with-profit and CDC designs) by embedding an explicit smoothing coefficient into a decumulation model and benchmarking against an unsmoothed payout. While smoothing slightly mitigates early downside risk, it ultimately amplifies long-run income volatility and forces higher equity allocations, undermining its stabilising purpose.

Building on this critique, the second contribution introduces a multi-payment probability-hedging framework for CDC schemes during retirement. By formulating a dynamic programming and Lagrange-multiplier approach, it jointly optimises investment and quantile hedging caps on annual payouts. The resulting closed form strategies improve median retirement income, reduce volatility, and control the probability of falling outside a target income corridor via synthetic call overlays, all while ensuring actuarial fairness.

Finally, the thesis proposes a novel market-neutral arbitrage overlay for CDC portfolios. Embedding an Ornstein–Uhlenbeck mean-reversion mechanism into a statistical arbitrage strategy, it decouples alpha generation from market beta. Solved under both quadratic and S-shaped (prospect-theoretic) utilities, the optimal control policies dynamically hedge gains when funding ratios exceed targets and pursue alpha when deficits arise. Empirical backtests on historical equity and bond data demonstrate that this approach enhances risk-adjusted returns, tail-risk resilience, and payout stability relative to buy-and-hold benchmarks.

Together, these studies provide a comprehensive toolkit for pension fund managers and regulators: first, exposing the shortcomings of opacity-driven smoothing; next, offering a tractable probability-hedging solution to stabilise incomes; and finally, delivering a market-neutral arbitrage framework that smooths retiree payouts without creating open-ended sponsor liabilities. The combined insights inform the design of transparent, equitable, and robust collective pension schemes.

Publication Type:	Thesis (Doctoral)
Subjects:	H Social Sciences > HA Statistics H Social Sciences > HB Economic Theory H Social Sciences > HD Industries. Land use. Labor > HD61 Risk Management H Social Sciences > HG Finance Q Science > QA Mathematics
Departments:	Bayes Business School > Bayes Business School Doctoral Theses Bayes Business School > Faculty of Actuarial Science & Insurance Doctoral Theses

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