Mean-Quadratic Variation Portfolio Optimization: A Desirable Alternative to Time-Consistent Mean-Variance Optimization?

Staden, Pieter M. van; Dang, Duy-Minh

doi:10.1137/18m1222570

Cited by 13 publications

(2 citation statements)

References 39 publications

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“…Finally, note that in the limit as t i − t i−1 → 0, the risk term on the right-hand side of (8.7) becomes a weighted portfolio quadratic variation. This has previously been suggested as a standalone risk measure in sources such as Brugiere (1996), Forsyth et al (2012), andvan Staden et al (2019).…”

Section: Analysis Of the Objective Functionmentioning

confidence: 99%

Optimal Asset Allocation for Dc Pension Decumulation With a Variable Spending Rule

Vetzal¹,

Westmacott²

2020

ASTIN Bull.

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We determine the optimal asset allocation to bonds and stocks using an annually recalculated virtual annuity (ARVA) spending rule for DC pension plan decumulation. Our objective function minimizes downside withdrawal variability for a given fixed value of total expected withdrawals. The optimal asset allocation is found using optimal stochastic control methods. We formulate the strategy as a solution to a Hamilton–Jacobi–Bellman (HJB) Partial Integro Differential Equation (PIDE). We impose realistic constraints on the controls (no-shorting, no-leverage, discrete rebalancing) and solve the HJB PIDEs numerically. Compared to a fixed-weight strategy which has the same expected total withdrawals, the optimal strategy has a much smaller average allocation to stocks and tends to de-risk rapidly over time. This conclusion holds in the case of a parametric model based on historical data and also in a bootstrapped market based on the historical data.

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Section: Analysis Of the Objective Functionmentioning

confidence: 99%

Optimal Asset Allocation for Dc Pension Decumulation With a Variable Spending Rule

Vetzal¹,

Westmacott²

2020

ASTIN Bull.

Self Cite

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“…Van Staden, P. M., D. Dang, and P. Forsyth (2019a). Mean-quadratic variation portfolio optimization: A desirable alternative to time-consistent mean-variance optimization?…”

Section: Conclusion Of This Chaptermentioning

confidence: 99%

Numerical methods for mean-risk portfolio optimization

Staden¹,

Marais²

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We consider various aspects of the dynamic mean-risk portfolio optimization problem, with specific focus on the numerical methods to solve this problem in the case where the risk measure is either the variance of wealth outcomes or the quadratic variation of the wealth process. In the case where the risk measure is the variance of wealth outcomes, the mean-risk problem is known as the dynamic mean-variance (MV) portfolio optimization problem. Since variance is not separable in the sense of dynamic programming, the MV objective violates Bellman's principle of optimality. As a result, the possibility of the time-inconsistency of the associated MV-optimal investment strategies leads to a number of competing approaches to formulating and solving the dynamic MV problem. We primarily focus on the two main approaches, namely the time-consistent MV (TCMV) and the pre-commitment MV (PCMV) optimization problems. In addition, this investigation also leads us to consider related approaches which are not necessarily MV optimal in some sense, such as the Mean-Quadratic Variation (MQV) portfolio optimization problem.

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A semi‐Lagrangian ε$$ \varepsilon $$‐monotone Fourier method for continuous withdrawal GMWBs under jump‐diffusion with stochastic interest rate

Lu,

Dang

2023

Numerical Methods Partial

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We develop an efficient pricing approach for guaranteed minimum withdrawal benefits (GMWBs) with continuous withdrawals under a realistic modeling setting with jump‐diffusions and stochastic interest rate. Utilizing an impulse stochastic control framework, we formulate the no‐arbitrage GMWB pricing problem as a time‐dependent Hamilton‐Jacobi‐Bellman (HJB) Quasi‐Variational Inequality (QVI) having three spatial dimensions with cross derivative terms. Through a novel numerical approach built upon a combination of a semi‐Lagrangian method and the Green's function of an associated linear partial integro‐differential equation, we develop an ‐monotone Fourier pricing method, where is a monotonicity tolerance. Together with a provable strong comparison result for the HJB‐QVI, we mathematically demonstrate convergence of the proposed scheme to the viscosity solution of the HJB‐QVI as . We present a comprehensive study of the impact of simultaneously considering jumps in the subaccount process and stochastic interest rate on the no‐arbitrage prices and fair insurance fees of GMWBs, as well as on the holder's optimal withdrawal behaviors.

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Mean-Quadratic Variation Portfolio Optimization: A Desirable Alternative to Time-Consistent Mean-Variance Optimization?

Cited by 13 publications

References 39 publications

Optimal Asset Allocation for Dc Pension Decumulation With a Variable Spending Rule

Optimal Asset Allocation for Dc Pension Decumulation With a Variable Spending Rule

Numerical methods for mean-risk portfolio optimization

A semi‐Lagrangian ε$$ \varepsilon $$‐monotone Fourier method for continuous withdrawal GMWBs under jump‐diffusion with stochastic interest rate

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