A defined benefit pension plan game with Brownian and Poisson jumps uncertainty

Producción CientíficaIn this paper, we study the optimal management of an aggregated pension fund of defined benefit type by means of a differential game with two players, the firm and the participants. We assume that the fund wealth is greater than the actuarial liability and then the manager builds a pension fund surplus. In order to contemplate sudden changes in the financial market, the surplus can be invested in a portfolio with a bond and several risky assets where the uncertainty comes from Brownian motions and Poisson processes. The aim of the participants is to maximize a utility of the extra benefits. The game is analyzed in three scenarios. In the first, the aim of the firm is to maximize a utility of the fund surplus, in the second, to minimize the probability that the fund surplus reaches a low level, and in the third, to minimize the expected time of reaching a benchmark surplus. An infinite horizon is considered, and the game is solved by means of the dynamic programming approach. The influence of the jumps of the financial market on the Nash equilibrium strategies and the fund surplus is studied by means of a numerical illustration

Mean-variance optimization problems for an accumulation phase in a defined benefit plan

In this paper we deal with contribution rate and asset allocation strategies in a pre-retirement accumulation phase. We consider a single cohort of workers and investigate a retirement plan of a defined benefit type in which an accumulated fund is converted into a life annuity. Due to the random evolution of a mortality intensity, the future price of an annuity, and as a result, the liability of the fund, is uncertain. A manager has control over a contribution rate and an investment strategy and is concerned with covering the random claim. We consider two mean–variance optimization problems, which are quadratic control problems with an additional constraint on the expected value of the terminal surplus of the fund. This functional objectives can be related to the well-established financial theory of claim hedging. The financial market consists of a risk-free asset with a constant force of interest and a risky asset whose price is driven by a Lévy noise, whereas the evolution of a mortality intensity is described by a stochastic differential equation driven by a Brownian motion. Techniques from the stochastic control theory are applied in order to find optimal strategies

Equilibrium strategies in a defined benefit pension plan game

Producción CientíficaWe study the optimal management of an aggregated overfunded pension plan of defined benefit type as a two-player noncooperative differential game. The model’s key fact is to consider the fund surplus as a strategic variable that makes the pension plan more attractive both for current and future participants. We let the worker participants to act collectively as a single player that claims a share of the surplus, and let the sponsoring firm act as the player that cares about the investment of the surplus fund assets. The union’s objective is to maximize the expected discounted utility of the extra benefits claimed. We solve this asymmetric game under two different assumptions on the preferences of the firm: in the first scenario, the firm aims to maximize expected discounted utility derived from fund surplus; while in the second scenario, the firm cares about minimizing the probability that the fund surplus reaches very low values.Este trabajo se ha hecho con ayuda de los proyectos del Ministerio de Economía Industria y Competitividad (Spain), ECO2017-86261-P , ECO2014-56384-P y MDM2014-0431, y de la Comunidad de Madrid MadEco-CM S2015/HUM-3444 y Comunidad de Castilla y León VA148G18

A public guarantee of a minimum return to defined contribution pension scheme members

The recent financial crisis has clearly demonstrated the exposure of defined contribution (DC) pension scheme members to extreme financial market risks. This paper argues that the government might offer DC plan members a minimum return guarantee, funded by risk based premia. Option pricing formulas show that the guarantee could be quite expensive, but public provision could reduce the costs borne by workers. Such an arrangement would be sustainable for the government and would give workers an acceptable benefit/contribution ratio in worst-case scenarios, while still allowing them to reap the advantages of occupational or individual funded pension schemes.defined contribution pension schemes, financial market tail risks, return guarantees, exchange option, ModiglianiÂ’s Treasury CFDB swap

Macroeconomic Volatility and Sovereign Asset-Liability Management

For most developing countries, the predominant source of sovereign wealth is commodity related export income. However, over-reliance on commodity related income exposes countries to significant terms of trade shocks due to excessive price volatility. The spillovers are pro-cyclical fiscal policies and macroeconomic volatility problems that if not adequately managed, could have catastrophic economic consequences including sovereign bankruptcy. The aim of this study is to explore new ways of solving the problem in an asset-liability management framework for an exporting country like Ghana. Firstly, I develop an unconditional commodity investment strategy in the tactical mean-variance setting for deterministic returns. Secondly, in continuous time, shocks to return moments induce additional hedging demands warranting an extension of the analysis to a dynamic stochastic setting whereby, the optimal commodity investment and fiscal consumption policies are conditioned on the stochastic realisations of commodity prices. Thirdly, I incorporate jumps and stochastic volatility in an incomplete market extension of the conditional model. Finally, I account for partial autocorrelation, significant heteroskedastic disturbances, cointegration and non-linear dependence in the sample data by adopting GARCH-Error Correction and dynamic Copula-GARCH models to enhance the forecasting accuracy of the optimal hedge ratios used for the state-contingent dynamic overlay hedging strategies that guarantee Pareto efficient allocation. The unconditional model increases the Sharpe ratio by a significant margin and noticeably improves the portfolio value-at-risk and maximum drawdown. Meanwhile, the optimal commodities investment decisions are superior in in-sample performance and robust to extreme interest rate changes by up to 10 times the current rate. In the dynamic setting, I show that momentum strategies are outperformed by contrarian policies, fiscal consumption must account for less than 40% of sovereign wealth, while risky investments must not exceed 50% of the residual wealth. Moreover, hedging costs are reduced by as much as 55% while numerically generating state-dependent dynamic futures hedging policies that reveal a predominant portfolio strategy analogous to the unconditional model. The results suggest buying commodity futures contracts when the country’s current exposure in a particular asset is less than the model implied optimal quantity and selling futures contracts when the actual quantity exported exceeds the benchmark.Open Acces

Four Essays in Equity-Linked Life and Pension Insurance : Financial Analysis of Surrender Guarantees, Pension Guarantee Funds and Pension Retirement Plans

In this dissertation we study three very important types of insurance, equity-linked life insurance with surrender guarantees, pension insurance and the insurance provided by (pension) insurance guarantee funds. In chapter 2 we study the market consistent valuation of equity linked life insurance contracts, particularly the valuation of a surrender option. In our model the policyholder can surrender exogenously and endogenously. More importantly, we model the realistic perspective that the surrender option value depends on the state of the economy. The state of the economy can represent financial market regimes, macroeconomic regimes or business cycles. The consideration of economic states is an important contribution since equity-linked life insurance contracts are long-dated and in the long run there can occur several structural changes in the economic conditions which considerably affect both the value of the underlying financial portfolio and most importantly the surrender behavior of the policyholder. Chapter 3 and chapter 4 are concerned with the (re)insurance of pension guarantee funds (PGF). These government imposed pension schemes provide (re)insurance to defined benefit (DB) plan holders in terms of paying pension benefits if the corresponding sponsoring company and the pension fund are insolvent. We study and model solution concepts for pension guarantee funds to better protect policyholders by reducing the risk exposure of their financial guarantee. We model two solution concepts. In chapter 3 we provide a formal model to compute a risk-based premium paid to the PGF under distress termination, the conventional type of termination, where a pension fund is closed due to the insolvency of the sponsoring company. We incorporate several realistic perspectives and compare our theoretical pricing formula for a sample of the largest US DB plan sponsors. In chapter 4 we study the other type of termination, involuntary termination. Under involuntary termination the PGF terminates a substantially underfunded DB plan. In that case the crucial question is when the PGF should optimally intervene. We determine an optimal timing of intervention in terms of a critical funding ratio of the insured DB pension fund. The basic idea of our model is that the PGF acts in the interest of the beneficiaries and maximizes their expected utility. In addition the PGF protects its financial guarantee by controlling two solvency requirements, the shortfall probability and the expected shortfall of the DB plan. In chapter 4 the DB plan is modeled more specifically and compared to the other main pension retirement plan, the defined contribution plan (DC plan). The analysis is conducted in an expected utility framework under different preferences by taking an essential tradeoff into account. Specifically, the policyholder faces salary risk in both retirement plans, he faces investment risk only in the DC plan and portability risk, the risk of losing benefits when changing the employer is mostly present in the DB plan. As a means of comparison we take the critical job switching intensity or more intuitively the average number of job moves after which the DC plan is preferred in expected utility terms

Long-term decision making in the presence of financial disasters

The research question focuses on three areas. First, what is the most appropriate model and estimation method for studying portfolio optimisation under tail risk with an aim towards managerial incentives. Second, how outcomes differ for investors who take jumps into account compared to those who do not. Third, how managerial incentives in the form of fees and compensation structures create a conflict of interest between investors and funds in the presence of jumps, leading to a need for policy suggestions. To answer those questions the thesis builds up from a CARA single-state model to an SV model to an SVCJ model with jumps in returns and volatility, leverage and heteroskedasticity. The model and its SV only counterpart are estimated via MCMC. A closed-form solution for the portfolio weights is derived and used in subsequent simulations. The results are that the investor always has an incentive to knowingly ignore tail risk in terms of wealth but never in terms of utility, the manager has an incentive in the short- and mid-run to undertake excess risk but not in the long-run, the criteria for the incentive horizon are risk aversion and how investor wealth moves between funds, and policy suggestions are made based on those grounds

Optimal Asset Allocation in a High Inflation Regime: a Leverage-feasible Neural Network Approach

We study the optimal multi-period asset allocation problem with leverage constraints in a persistent, high-inflation environment. Based on filtered high-inflation regimes, we discover that a portfolio containing an equal-weighted stock index partially stochastically dominates a portfolio containing a capitalization-weighted stock index. Assuming the asset prices follow the jump diffusion model during high inflation periods, we establish a closed-form solution for the optimal strategy that outperforms a passive strategy under the cumulative quadratic tracking difference (CD) objective. The closed-form solution provides insights but requires unrealistic constraints. To obtain strategies under more practical considerations, we consider a constrained optimal control problem with bounded leverage. To solve this optimal control problem, we propose a novel leverage-feasible neural network (LFNN) model that approximates the optimal control directly. The LFNN model avoids high-dimensional evaluation of the conditional expectation (common in dynamic programming (DP) approaches). We establish mathematically that the LFNN approximation can yield a solution that is arbitrarily close to the solution of the original optimal control problem with bounded leverage. Numerical experiments show that the LFNN model achieves comparable performance to the closed-form solution on simulated data. We apply the LFNN approach to a four-asset investment scenario with bootstrap resampled asset returns. The LFNN strategy consistently outperforms the passive benchmark strategy by about 200 bps (median annualized return), with a greater than 90% probability of outperforming the benchmark at the terminal date. These results suggest that during persistent inflation regimes, investors should favor short-term bonds over long-term bonds, and the equal-weighted stock index over the cap-weighted stock index

Portfolio optimization in a defined benefit pension plan where the risky assets are processes with constant elasticity of variance

The paper studies the optimal asset allocation problem of a defined benefit pension plan that operates in a financial market composed of risky assets whose prices are constant elasticity variance processes. The benefits paid to the participants are deterministic. The contributions to the fund are designed by a spread amortization method, which takes into account the size of the unfunded actuarial liability, defined as the difference between the actuarial liability and the fund assets.We address the case where the fund manager wishes to minimize the solvency risk at the final date of the plan when the fund is underfunded, as well as the case where the fund manager wishes to maximize an increasing, constant elasticity utility function of the fund surplus, when the fund is overfunded. The optimal portfolio and contributions are obtained in both scenarios, with the help of the Hamilton–Jacobi–Bellman equation. A numerical illustration shows the evolution of the plan for several values of the elasticity parameter of the CEV price processes and the risk aversion of the manager, yielding some tips on the main properties of the optimal portfolio.Este trabajo se ha hecho con ayuda de los proyectos de la Consejería de Educación de la Junta de Castilla y León (VA148G18), de la Comunidad de Madrid (MadEcoCM S2015/HUM-3444) y del Ministerio de Economía y Competitividad (ECO2011-24200, ECO2014-56384-P, MDM 2014- 0431 y ECO2017-86261-P)

Institutional and individual investors: Saving for old age

This paper brings together the academic literature on individual and institutional investors in order to understand the nature of difficulties faced by them and set the background for the Special Issue. This introductory article and the papers in the Special Issue contribute to the debate on how to support individuals in their savings commitments and investment decision-making and whether and how institutional investors have fulfilled their role in supporting the development of the funded pension industry. There are three main conclusions: (i) individual investors are not ready for the role that has been assigned to them in the pension industry, (ii) institutional investors are a long way short of establishing healthy relational contracts and trustworthy relationships with their clients, and (iii) more effective regulation may be needed