Marina Di Giacinto

Pension Funds with a Minimum Guarantee: A Stochastic Control Approach

In this paper we propose and study a continuous-time stochastic model of optimal allocation for a defined contribution pension fund with a minimum guarantee. We adopt the point of view of a fund manager maximizing the expected utility from the fund wealth over an infinite horizon. In our model the dynamics of wealth takes directly into account the flows of contributions and benefits, and the level of wealth is constrained to stay above a “solvency level.” The fund manager can invest in a riskless asset and in a risky asset, but borrowing and short selling are prohibited. We concentrate the analysis on the effect of the solvency constraint, analyzing in particular what happens when the fund wealth reaches the allowed minimum value represented by the solvency level.The model is naturally formulated as an optimal stochastic control problem with state constraints and is treated by the dynamic programming approach. We show that the value function of the problem is a regular solution of the associated Hamilton–Jacobi–Bellman equation. Then we apply verification techniques to get the optimal allocation strategy in feedback form and to study its properties. We finally give a special example with explicit solution.

Constrained Portfolio Choices in the Decumulation Phase of a Pension Plan

This paper deals with a constrained investment problem for a defined contribution (DC) pension fund where retirees are allowed to defer the purchase of the annuity at some future time after retirement. This problem has already been treated in the unconstrained case in a number of papers. The aim of this work is to deal with the more realistic case when constraints on the investment strategies and on the state variable are present. Due to the difficulty of the task, we consider the basic model of [Gerrard, Haberman & Vigna, 2004], where interim consumption and annuitization time are fixed. The main goal is to find the optimal portfolio choice to be adopted by the retiree from retirement to annuitization time in a Black and Scholes financial market. We define and study the problem at two different complexity levels. In the first level (problem P1), we only require no short-selling. In the second level (problem P2), we add a constraint on the state variable, by imposing that the final fund cannot be lower than a certain guaranteed safety level. This implies, in particular, no ruin. The mathematical problem is naturally formulated as a stochastic control problem with constraints on the control and the state variable, and is approached by the dynamic programming method. We give a general result of existence and uniqueness of regular solutions for the Hamilton-Jacobi-Bellman equation and, in a special case, we explicitly compute the value function for the problem and give the optimal strategy in feedback form. A numerical application of the special case - when explicit solutions are available - ends the paper and shows the extent of applicability of the model to a DC pension fund in the decumulation phase.

Idiosyncratic Learning, Creative Consumption and Well-Being

The consensus view is that economists should observe consumer choices and abstain from investigating the psychological and physiological causes of wants, or the mechanisms governing the formation of preferences. This may be a correct procedure as far as ordinary functional goods are concerned. Problems tend to arise with creative goods (e.g. cultural goods) whose consumption (i) requires skills acquired through education and experience and (ii) generates positive and negative feedbacks and learning-by-consuming processes. This paper presents a simple model of local learning explaining the idiosyncratic accumulation of consumption human capital. Consumption generates local feedback mechanisms whose characteristics depend on the nature of goods and on the type of agent. The model provides some insights on the microeconomics of creative consumption and on the specific role of education.

Optimal Execution with Uncertain Order Fills in Almgren-Chriss Framework

The classical price impact model of Almgren and Chriss is extended to incorporate the uncertainty of order fills. The extended model can be recast as alternatives to uncertain impact models and stochastic liquidity models. Optimal strategies are determined by maximizing the expected final profit and loss (P&L) and various P&L-risk tradeoffs including utility maximization. Closed form expressions for optimal strategies are obtained in linear cases. The results suggest a type of adaptive volume weighted average price, adaptive percentage of volume and adaptive Almgren–Chriss strategies. VWAP and classical Almgren–Chriss strategies are recovered as limiting cases with a different characteristic time scale of liquidation for the latter.

Credence goods, consumers’ trust in regulation and high quality exports

We analyze the impact of the effectiveness of internal regulation for the development of internal and export markets for credence goods, focusing on food products, particularly for a developing country which is an exporter (or a potential exporter). In the model, since goods of actual different quality can be sold as high quality goods, expected quality is a function of consumers’ beliefs about the effectiveness of regulation. Foreign consumers, who cannot observe foreign regulation as closely as domestic ones, may partly base their expectations on the level of development of the exporting country. Low effectiveness, negative stereotype and low consumers’ trust may cause a failure in the market for high quality, and there may be a trap of underdevelopment and no high quality exports. The main policy implications are that increasing the effectiveness of regulation improves export prospects; standard setting and enforcement by external actors, such as supermarkets, or NGOs in the case of certain niche markets, is likely to be beneficial.