Optimal partition of a large labor force into working pairs

Kremer and Maskin (Wage inequality and segregation by skill. Working Paper 5718, National Bureau of Economic Research, , 1996) introduced an idealized model for pairing workers and managers with different skill levels into small teams selected to maximize productivity. They used it to analyze the impact of technological change and widening skill gaps on labor market segregation. The present paper extends their model to a workforce with multidimensional skill types, continuously distributed, and gives a mathematical analysis of the extension. Pure and mixed notions of optimal pairing are introduced, which play an important role in the formulation and analysis of the model. The existence and uniqueness of such pairings are established using techniques from the theory of optimal transportation and infinite-dimensional linear programming.     

Pricing a contingent claim liability with transaction costs using asymptotic analysis for optimal investment

We price a contingent claim liability (claim for short) using a utility indifference argument. We consider an agent with exponential utility, who invests in a stock and a money market account with the goal of maximizing the utility of his investment at the final time T in the presence of a proportional transaction cost ε>0 in two cases: with and without a claim. Using the heuristic computations of Whalley and Wilmott (Math. Finance 7:307–324, 1997), under suitable technical conditions, we provide a rigorous derivation of the asymptotic expansion of the value function in powers of \(\varepsilon^{\frac{1}{3}}\) in both cases with and without a claim. Additionally, using the utility indifference method, we derive the price of the claim at the leading order of \(\varepsilon^{\frac{2}{3}}\) . In both cases, we also obtain a “nearly optimal” strategy, whose expected utility asymptotically matches the leading terms of the value function. We also present an example of how this methodology can be used to price more exotic barrier-type contingent claims.     

Portfolio optimization under convex incentive schemes

We consider the terminal wealth utility maximization problem from the point of view of a portfolio manager who is paid by an incentive scheme, which is given as a convex function g of the terminal wealth. The manager’s own utility function U is assumed to be smooth and strictly concave; however, the resulting utility function U°g fails to be concave. As a consequence, the problem considered here does not fit into the classical portfolio optimization theory. Using duality theory, we prove wealth-independent existence and uniqueness of the optimal portfolio in general (incomplete) semimartingale markets as long as the unique optimizer of the dual problem has a continuous law. In many cases, this existence and uniqueness result is independent of the incentive scheme and depends only on the structure of the set of equivalent local martingale measures. As examples, we discuss (complete) one-dimensional models as well as (incomplete) lognormal mixture and popular stochastic volatility models. We also provide a detailed analysis of the case where the unique optimizer of the dual problem does not have a continuous law, leading to optimization problems whose solvability by duality methods depends on the initial wealth of the investor.     

Investment horizon,risk, and compensation in the banking industry

This paper examines the relation between the investment horizon of banks and their CEO compensation, and its consequences for risk and performance. We find that banks with short-term investment intensity pay more cash bonus, exhibit higher risk and perform more poorly than banks with longer-term investment intensity. This evidence is broadly consistent with the view that short-term means of compensation encouraged a short-term investment focus, which in turn led to both higher risk and resulted in poorer performance, culminating in the sub-prime crisis. The inverse risk-performance relation suggests pay schemes were incongruent with shareholders’ interest. Moreover, pay arrangements used in banks prior to the subprime crisis exposed banks to the ex-post settling up problem (the clawback problem).     

Optimal investment with correlated stochastic volatility factors

The problem of portfolio allocation in the context of stocks evolving in random environments, that is with volatility and returns depending on random factors, has attracted a lot of attention. The problem of maximizing a power utility at a terminal time with only one random factor can be linearized thanks to a classical distortion transformation. In the present paper, we address the situation with several factors using a perturbation technique around the case where these factors are perfectly correlated reducing the problem to the case with a single factor. Our proposed approximation requires to solve numerically two linear equations in lower dimension instead of a fully nonlinear HJB equation. A rigorous accuracy result is derived by constructing sub- and super-solutions so that their difference is at the desired order of accuracy. We illustrate our result with a particular model for which we have explicit formulas for the approximation. In order to keep the notations as explicit as possible, we treat the case with one stock and two factors and we describe an extension to the case with two stocks and two factors.     

Trade spends and profitability of promotions

This paper examines the prevalent mechanism of financing advertising and temporary price reductions through trade spend budgets. A manufacturer and a retailer interact for a number of periods with a plan to hold a sale in the last period. During the nonpromotional periods, the retailer accumulates the funds in this budget in proportion to the size of its order from the manufacturer. In the sale period, the budget is used to finance the discount offered by the manufacturer and advertising. I find that the manufacturer drops its price in the sale period to increase the profitability of promotions for the retailer. To be able to sell more units during the sale period, the retailer needs to accumulate a larger trade spend. This is accomplished by setting a smaller mark-up over the manufacturer's price in the regular periods. The manufacturer takes advantage of the retailer's softer pricing by increasing its regular wholesale price. As long as such trade spends are used to finance advertising, the total profits of each firm increase. Using fixed trade spends, where the manufacturer allocates a fixed amount for the retailer, does not lead to an increase in profits.