OPTIMAL INVESTMENT WITH AN UNBOUNDED RANDOM ENDOWMENT AND UTILITY-BASED PRICING

This paper studies the problem of maximizing the expected utility of terminal wealth for a financial agent with an unbounded random endowment, and with a utility function which supports both positive and negative wealth. We prove the existence of an optimal trading strategy within a class of permissible strategies—those strategies whose wealth process is a super-martingale under all pricing measures with finite relative entropy. We give necessary and sufficient conditions for the absence of utility-based arbitrage, and for the existence of a solution to the primal problem. We consider two utility-based methods which can be used to price contingent claims. Firstly we investigate marginal utility-based price processes (MUBPP's). We show that such processes can be characterized as local martingales under the normalized optimal dual measure for the utility maximizing investor. Finally, we present some new results on utility indifference prices, including continuity properties and volume asymptotics for the case of a general utility function, unbounded endowment and unbounded contingent claims.     

MULTIPLICATIVE APPROXIMATION OF WEALTH PROCESSES INVOLVING NO‐SHORT‐SALES STRATEGIES VIA SIMPLE TRADING

A financial market model with general semimartingale asset–price processes and where agents can only trade using no‐short‐sales strategies is considered. We show that wealth processes using continuous trading can be approximated very closely by wealth processes using simple combinations of buy‐and‐hold trading. This approximation is based on controlling the proportions of wealth invested in the assets. As an application, the utility maximization problem is considered and it is shown that optimal expected utilities and wealth processes resulting from continuous trading can be approximated arbitrarily well by the use of simple combinations of buy‐and‐hold strategies.     

OPTIMALITY AND STATE PRICING IN CONSTRAINED FINANCIAL MARKETS WITH RECURSIVE UTILITY UNDER CONTINUOUS AND DISCONTINUOUS INFORMATION

We study marginal pricing and optimality conditions for an agent maximizing generalized recursive utility in a financial market with information generated by Brownian motion and marked point processes. The setting allows for convex trading constraints, non-tradable income, and non-linear wealth dynamics. We show that the FBSDE system of the general optimality conditions reduces to a single BSDE under translation or scale invariance assumptions, and we identify tractable applications based on quadratic BSDEs. An appendix relates the main optimality conditions to duality.     

DISUTILITY, OPTIMAL RETIREMENT, AND PORTFOLIO SELECTION

We study the optimal retirement and consumption/investment choice of an infinitely-lived economic agent with a time-separable von Neumann–Morgenstern utility. A particular aspect of our problem is that the agent has a retirement option. Before retirement the agent receives labor income but suffers a utility loss from labor. By retiring, he avoids the utility loss but gives up labor income. We show that the agent retires optimally if his wealth exceeds a certain critical level. We also show that the agent consumes less and invests more in risky assets when he has an option to retire than he would in the absence of such an option.
An explicit solution can be provided by solving a free boundary value problem. In particular, the critical wealth level and the optimal consumption and portfolio policy are provided in explicit forms.     

OPTIMAL TIMING FOR AN INDIVISIBLE ASSET SALE

In this paper, we investigate the pricing via utility indifference of the right to sell a non‐traded asset. Consider an agent with power utility who owns a single unit of an indivisible, non‐traded asset, and who wishes to choose the optimum time to sell this asset. Suppose that this right to sell forms just part of the wealth of the agent, and that other wealth may be invested in a complete frictionless market. We formulate the problem as a mixed stochastic control/optimal stopping problem, which we then solve. We determine the optimal behavior of the agent, including the optimal criteria for the timing of the sale. It turns out that the optimal strategy is to sell the non‐traded asset the first time that its value exceeds a certain proportion of the agent's trading wealth. Further, it is possible to characterize this proportion as the solution to a transcendental equation.     

Collusion among many agents

In this paper we examine under a variety of contractual and informational settings how the addition of an additional agent affects the moral hazard problem between a principal and an agent. We find that there are circumstances when, even though the second agent can provide perfect information about the actions of the first agent, and vice versa, there is still a possibility that a wealth transfer from the principal to agents will occur. We later show that through an appropriate bonus-penalty scheme that a prisoner's dilemma situation can be created that eliminates any possibility of a wealth transfer. This paper differs from other recent works in this area in that it explicitly allows for collusive behavior and does not require that the principal know the explicit form of the agents' utility functions.     

OPTIMAL PORTFOLIO, CONSUMPTION-LEISURE AND RETIREMENT CHOICE PROBLEM WITH CES UTILITY

We study optimal portfolio, consumption-leisure and retirement choice of an infinitely lived economic agent whose instantaneous preference is characterized by a constant elasticity of substitution (CES) function of consumption and leisure. We integrate in one model the optimal consumption-leisure-work choice, the optimal portfolio selection, and the optimal stopping problem in which the agent chooses her retirement time. The economic agent derives utility from both consumption and leisure, and is able to adjust her supply of labor flexibly above a certain minimum work-hour, and also has a retirement option. We solve the problem analytically by considering a variational inequality arising from the dual functions of the optimal stopping problem. The optimal retirement time is characterized as the first time when her wealth exceeds a certain critical level. We provide the critical wealth level for retirement and characterize the optimal consumption-leisure and portfolio policies before and after retirement in closed forms. We also derive properties of the optimal policies. In particular, we show that consumption in general jumps around retirement.     

NO MARGINAL ARBITRAGE OF THE SECOND KIND FOR HIGH PRODUCTION REGIMES IN DISCRETE TIME PRODUCTION–INVESTMENT MODELS WITH PROPORTIONAL TRANSACTION COSTS

We consider a class of production–investment models in discrete time with proportional transaction costs. For linear production functions, we study a natural extension of the no‐arbitrage of the second kind condition introduced by Rásonyi. We show that this condition implies the closedness of the set of attainable claims and is equivalent to the existence of a strictly consistent price system under which the evaluation of future production profits is strictly negative. This allows us to discuss the closedness of the set of terminal wealth in models with nonlinear production, functions which may admit arbitrages of the second kind for low production regimes but not marginally for high production regimes.     

MODELING LIQUIDITY EFFECTS IN DISCRETE TIME

We study optimal portfolio choices for an agent with the aim of maximizing utility from terminal wealth within a market with liquidity costs. Under some mild conditions, we show the existence of optimal portfolios and that the marginal utility of the optimal terminal wealth serves as a change of measure to turn the marginal price process of the optimal strategy into a martingale. Finally, we illustrate our results numerically in a Cox–Ross–Rubinstein binomial model with liquidity costs and find the reservation ask prices for simple European put options.     

The Intergenerational Propagation of Wealth Inequality

This paper highlights the crucial role of demographic assumptions in models of the intergenerational transmission of wealth inequality. Specifically, we show that Alan Blinder's surprising predictions that bequest and mating practices can sustain but cannot cause wealth inequality are extremely fragile. We show that these predictions depend on a common and apparently minor demographic assumption: fixed sex ratios in family composition. We implement the Blinder model as an agent‐based simulation and show that without this demographic assumption such familial institutions are causative for wealth inequality, even in the long run.     

Business History and the Business–Man

This paper refutes the hypothesis put forward by W.D. Rubinstein that a disproportionately large share of Britain's wealth makers were active in commercial and financial trades in London. We use a data set of businessmen active in nineteenth- and early twentieth-century Britain and quantitative methods to show that the pattern of wealth holding was much more diverse than supposed by Rubinstein. A large fortune could be made in a variety of regions and occupations. Big industrialists active in the provinces were equally capable of generating wealth similar in size and significance to the City elite. More generally, London was not the centre of wealth making in this period. Neither was there a subordination of industrial and manufacturing to commercial and financial wealth.     

Toward Dynamic Corporate Stakeholder Responsibility

Today, sustainable relations with a broad range of key stakeholders are not only important from a normative business ethics perspective, but also from an entrepreneurial viewpoint to allow and support the long-term survival of a firm. We will argue that the traditional conception of a firm’s corporate social responsibility does not reflect this view and that a comprehensive and dynamic conception of a firm’s responsibilities is necessary to map the reality of business practice and to manage the challenges implied by sustainability. We think that distributive justice, that is the way in which firms involve their stakeholders in their wealth creation and dissemination processes, provides a comprehensive understanding of corporate responsibilities. Concerning procedural justice, we will discuss how firms involve stakeholders in their strategic processes according to their contribution to wealth creation. In the course of the article, we will propose a framework along with three design principles that can be used for shaping dynamic and comprehensive corporate responsibilities, and which thereby allow a sustainable procedure for changing business and non-business environments.     

LINKED RECURSIVE PREFERENCES AND OPTIMALITY

We study a class of optimization problems involving linked recursive preferences in a continuous‐time Brownian setting. Such links can arise when preferences depend directly on the level or volatility of wealth, in principal–agent (optimal compensation) problems with moral hazard, and when the impact of social influences on preferences is modeled via utility (and utility diffusion) externalities. We characterize the necessary first‐order conditions, which are also sufficient under additional conditions ensuring concavity. We also examine applications to optimal consumption and portfolio choice, and applications to Pareto optimal allocations.     

RISK-AVERSION BEHAVIOR IN CONSUMPTION/INVESTMENT PROBLEMS1

In this paper, we study the risk-aversion behavior of an agent in the dynamic framework of consumption/investment decision making that allows the possibility of bankruptcy. Agent's consumption utility is assumed to be represented by a strictly increasing, strictly concave, continuously differentiable function in the general case and by a HARA-type function in the special case treated in the paper. Coefficients of absolute and relative risk aversion are defined to be the well-known curvature measures associated with the derived utility of wealth obtained as the value function of the agent's optimization problem. Through an analysis of these coefficients, we show how the change in agent's risk aversion as his wealth changes depends on his consumption utility and the other problem parameters, including the payment at bankruptcy. Moreover, in the HARA case, we can conclude that the agent's relative risk aversion is nondecreasing with wealth, while his absolute risk aversion is decreasing with wealth only if he is sufficiently wealthy. At lower wealth levels, however, the agent's absolute risk aversion may increase with wealth in some cases.     

MULTIDIMENSIONAL PORTFOLIO OPTIMIZATION WITH PROPORTIONAL TRANSACTION COSTS

We provide a computational study of the problem of optimally allocating wealth among multiple stocks and a bank account, to maximize the infinite horizon discounted utility of consumption. We consider the situation where the transfer of wealth from one asset to another involves transaction costs that are proportional to the amount of wealth transferred. Our model allows for correlation between the price processes, which in turn gives rise to interesting hedging strategies. This results in a stochastic control problem with both drift-rate and singular controls, which can be recast as a free boundary problem in partial differential equations. Adapting the finite element method and using an iterative procedure that converts the free boundary problem into a sequence of fixed boundary problems, we provide an efficient numerical method for solving this problem. We present computational results that describe the impact of volatility, risk aversion of the investor, level of transaction costs, and correlation among the risky assets on the structure of the optimal policy. Finally we suggest and quantify some heuristic approximations.     

Realization utility with adaptive reference points

Experimental studies have demonstrated that a typical investor derives utility of the gain and loss, relative to certain reference point, realized at each sale of a stock, and that the reference point adapts asymmetrically to the stock's prior gains and losses in that the adaptation to a gain is more substantial than to a comparable loss. This empirical finding motivates us to consider a dynamic trading problem in which an agent decides when to sequentially sell and buy a stock in order to maximize her utility of terminal wealth and realized gains and losses based on a reference point that adapts asymmetrically to the stock's prior gains and losses. We show that this agent is more reluctant to sell the stock at a loss than another agent whose reference point does not adapt to the stock gain or loss at all, leading to a higher percentage of gains realized (PGR) and a lower percentage of losses realized (PLR). We also show that when the agent weighs the utility of realized gains and losses more heavily in her investment criteria, she trades the stock more frequently, the PGR becomes lower, and the PLR becomes higher.     

Wealth,Exploitation and Labor Discipline in the Contemporary Capitalist Economy

This paper synthesizes in a Leontief economic model the arguments of exploitation and unequal distribution of wealth put forward by Roemer (1982, 1986) and of the power relationship between employers and employees with regard to the performance of labor presented by Bowles and Gintis (1988, 1990). The author introduces the level of the agent’s labor-discipline as measured by the ratio of labor effort per unit of labor time to the real wage rate. The connection bet ween this kind of power index and both exploitation status and wealth distribution is then examined. The result obtained is that, under some reasonable assumptions, the exploitation status and the level of labor-discipline accurately reflect the unequal distribution of wealth.     

NO-FREE-LUNCH EQUIVALENCES FOR EXPONENTIAL LÉVY MODELS UNDER CONVEX CONSTRAINTS ON INVESTMENT

We provide equivalence of numerous no-free-lunch type conditions for financial markets where the asset prices are modeled as exponential Lévy processes, under possible convex constraints in the use of investment strategies. The general message is the following: if any kind of free lunch exists in these models it has to be of the most egregious type, generating an increasing wealth. Furthermore, we connect the previous to the existence of the numéraire portfolio , both for its particular expositional clarity in exponential Lévy models and as a first step in obtaining analogues of the no-free-lunch equivalences in general semimartingale models, a task that is taken on in Karatzas and Kardaras (2007) .     

Optimal Portfolios with Bounded Capital at Risk

We consider some continuous-time Markowitz type portfolio problems that consist of maximizing expected terminal wealth under the constraint of an upper bound for the capital at risk. In a Black–Scholes setting we obtain closed-form explicit solutions and compare their form and implications to those of the classical continuous-time mean-variance problem. We also consider more general price processes that allow for larger fluctuations in the returns.     

Does Student Loan Debt Contribute to Racial Wealth Gaps? A Decomposition Analysis

There is evidence of a large and growing student debt burden over the last decade. Previous research has shown that the presence of student debt jeopardized the short‐term financial wealth of U.S. households during the Great Recession. We examine the effects of student loan use on the wealth of U.S. households post‐recession, using recent data from the 2013 and 2016 Survey of Consumer Finances. We find that mean 2016 wealth for households with no outstanding student debt is more than four times higher than households with student debt. We find that living in a household at the 15th, 30th, 50th, 70th, and 85th percentile of the wealth distribution with student debt is associated with an 80%, 49%, 37%, 35%, and 36% wealth loss compared with a similar household with no student debt. Our decomposition results suggest that student loan use can explain between 3% and 7% of the Black‐White wealth gap across the wealth distribution but is insignificant in explaining the Hispanic‐White wealth gap.