Pension Funds with a Minimum Guarantee: A Stochastic Control Approach

Giacinto, Marina Di; Gozzi, Fausto; Federico, Salvatore

doi:10.2139/ssrn.960459

Cited by 17 publications

(25 citation statements)

References 42 publications

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“…It must be said that imposing a priori restrictions on the controls would change substantially the formulation of the problem and would make it very difficult to tackle mathematically. To the best of our knowledge, the only work where an optimization problem with constraints has been thoroughly treated in the accumulation phase of a DC scheme is Di Giacinto et al (2011). Table 9 reports for the four strategies considered some percentiles of the distribution of the final wealth, its mean and standard deviation, the probability of reaching the target and the mean shortfall, defined as the mean of the deviation of the fund from the target, given that the target is not reached.…”

Section: Numerical Simulations To Understand the Impact Of VImentioning

confidence: 99%

“…The literature on the accumulation phase of defined contribution pension schemes is full of examples of optimal investment strategies resulting from EU maximization. See, for instance, Boulier, Huang & Taillard (2001), Haberman & Vigna (2002), Deelstra, Grasselli & Koehl (2003), Devolder, Bosch Princep & Dominguez Fabian (2003), Battocchio & Menoncin (2004), Cairns, Blake & Dowd (2006), Xiao, Zhai & Qin (2007), Gao (2008), Di Giacinto, Federico & Gozzi (2011).…”

Section: Introductionmentioning

confidence: 99%

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On efficiency of mean–variance based portfolio selection in defined contribution pension schemes

Vigna

2012

Quantitative Finance

103

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We consider the portfolio selection problem in the accumulation phase of a defined contribution (DC) pension scheme. We solve the mean-variance portfolio selection problem using the embedding technique pioneered by Zhou & Li (2000) and show that it is equivalent to a targetbased optimization problem, consisting in the minimization of a quadratic loss function. We support the use of the target-based approach in DC pension funds for three reasons. Firstly, it transforms the difficult problem of selecting the individual's risk aversion coefficient into the easier task of choosing an appropriate target. Secondly, it is intuitive, flexible and adaptable to the member's needs and preferences. Thirdly, it produces final portfolios that are efficient in the mean-variance setting.We address the issue of comparison between an efficient portfolio and a portfolio that is optimal according to the more general criterion of maximization of expected utility (EU). The two natural notions of Variance Inefficiency and Mean Inefficiency are introduced, which measure the distance of an optimal inefficient portfolio from an efficient one, focusing on their variance and on their expected value, respectively. We illustrate the general procedure for finding the mean-variance inefficiency for the HARA class of utility functions, and then focus on the popular classes of CARA and CRRA utility functions. In these cases we prove the intuitive but not trivial results that the mean-variance inefficiency decreases with the risk aversion of the individual and increases with the time horizon and the Sharpe ratio of the risky asset. As a byproduct we prove that the CARA and CRRA optimal portfolio are not mean-variance efficient.Numerical investigations stress the impact of the time horizon on the extent of mean-variance inefficiency of CARA and CRRA utility functions. While at instantaneous level EU-optimality and efficiency coincide (see Merton (1971)), we find that for short durations they do not differ significantly. However, for longer durations -that are typical in pension funds -the extent of inefficiency turns out to be remarkable and should be taken into account by pension fund investment managers seeking appropriate rules for portfolio selection. Indeed, we see this result as a fourth reason for supporting the use of the target-based approach in DC pension schemes.

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Section: Numerical Simulations To Understand the Impact Of VImentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

On efficiency of mean–variance based portfolio selection in defined contribution pension schemes

Vigna

2012

Quantitative Finance

103

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“…To overcome this problem, we approximate the function ϕ i (and so v(x, y, i)) as follows. We define, for every ε > 0 a function ϕ ε = (ϕ ε ) i∈I d ∈ C 2 ([0, 1], R d ) as in the proof of Theorem 4.24 in [6], such that…”

Section: Regularity Results and Verification Theoremmentioning

confidence: 99%

“…✷ Remark 3.1 The above proof of continuity of the value functions at the boundary by means of the dynamic programming principle is somehow different from other similar proofs that one can find e.g. in [6,17,23]. Indeed in such problems the proof of dynamic programming principle is done (or referred to) in two parts: the "easy" one (≤) which does not require continuity of the value function, and the 'difficult" one (≥) which requires the continuity of the value function up to the boundary.…”

Section: Some Properties Of the Value Functionmentioning

confidence: 88%

Investment/Consumption Problem in Illiquid Markets with Regime-Switching

Gassiat¹,

Gozzi²,

Pham³

2014

SIAM J. Control Optim.

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We consider an illiquid financial market with different regimes modeled by a continuous-time finite-state Markov chain. The investor can trade a stock only at the discrete arrival times of a Cox process with intensity depending on the market regime. Moreover, the risky asset price is subject to liquidity shocks, which change its rate of return and volatility, and induce jumps on its dynamics. In this setting, we study the problem of an economic agent optimizing her expected utility from consumption under a nonbankruptcy constraint. By using the dynamic programming method, we provide the characterization of the value function of this stochastic control problem in terms of the unique viscosity solution to a system of integro-partial differential equations. We next focus on the popular case of CRRA utility functions, for which we can prove smoothness C 2 results for the value function. As an important byproduct, this allows us to get the existence of optimal investment/consumption strategies characterized in feedback forms. We analyze a convergent numerical scheme for the resolution to our stochastic control problem, and we illustrate finally with some numerical experiments the effects of liquidity regimes in the investor's optimal decision.

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“…They minimize the quadratic loss gained from the performance variable, which is defined as the optimal portfolio over the target benchmark portfolio [23]. Di-Giacinto et al solve a portfolio selection problem with a minimum guarantee for a defined contribution pension fund [24]. Moreover, Gerrard et al [19] study the problem of maximizing the expected utility of the difference between the terminal wealth and the fixed guarantee.…”

Section: Introductionmentioning

confidence: 99%

An Optimal Turkish Private Pension Plan with a Guarantee Feature

İşcanog̃lu-Çekiç

2016

Risks

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Abstract:The Turkish Private Pension System is an investment system which aims to generate income for future consumption. This is a volunteer system, and the contributions are held in individual portfolios. Therefore, management of the funds is an important issue for both the participants and the insurance company. In this study, we propose an optimal private pension plan with a guarantee feature that is based on Constant Proportion Portfolio Insurance (CPPI). We derive a closed form formula for the optimal strategy with the help of dynamic programming. Moreover, our model is evaluated with numerical examples, and we compare its performance by implementing a sensitivity analysis.

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Pension Funds with a Minimum Guarantee: A Stochastic Control Approach

Cited by 17 publications

References 42 publications

On efficiency of mean–variance based portfolio selection in defined contribution pension schemes

On efficiency of mean–variance based portfolio selection in defined contribution pension schemes

Investment/Consumption Problem in Illiquid Markets with Regime-Switching

An Optimal Turkish Private Pension Plan with a Guarantee Feature

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