Contributions published at Quantitative Business Administration

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We compare asset allocations derived for cumulative prospect theory(CPT) based on two different methods: Maximizing CPT along the mean–variance efficient frontier and maximizing it without that restriction. We find that with normally distributed returns the difference is negligible. However, using standard asset allocation data of pension funds the difference is considerable. Moreover, with derivatives like call options the restriction to the mean-variance efficient frontier results in a sizable loss of e.g. expected return and expected utility.

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Coherent risk measures play an important role in building and solving optimization models for decision problems under uncertainty. We consider an extension to multiple time periods, where a risk-adjusted value for a stochastic process is recursively defined over the time steps, which ensures time consistency. A prominent example of a single-period coherent risk measure that is widely used in applications is Conditional-Value-at-Risk (CVaR). We show that a recursive calculation of CVaR leads to stochastic linear programming formulations. For the special case of the risk-adjusted value of a random variable at the time horizon, a lower bound is given. The possible integration of the risk-adjusted value into multi-stage mean-risk optimization problems is outlined.

Static and dynamic games are important tools for the analysis of strategic interactions among economic agents and have found many applications in economics. In many games, equilibria can be described as solutions of polynomial equations. In this paper, we describe state-of-the-art techniques for finding all solutions of polynomial systems of equations, and illustrate these techniques by computing all equilibria of both static and dynamic games with continuous strategies. We compute the equilibrium manifold for a Bertrand pricing game in which the number of equilibria changes with the market size. Moreover, we apply these techniques to two stochastic dynamic games of industry competition and check for equilibrium uniqueness.

We compare asset prices in an overlapping generations model for incomplete and complete markets. Individuals within a generational cohort have heterogeneous beliefs about future states of the economy and thus would like to make bets against each other. In the incomplete-markets economy, agents cannot make such bets. Asset price volatility is very small. The situation changes dramatically when markets are completed through financial innovations as the set of available securities now allows agents with different beliefs to place bets against each other. Wealth shifts across agents and generations. Such changes in the wealth distribution lead to substantial asset price volatility.

There are two important rules to patent races: minimal accomplishment necessary to receive the patent and the allocation of the innovation benefits. We study the optimal combination of these rules. A planner, who cannot distinguish between competing firms in a multistage innovation race, chooses the patent rules by maximizing either consumer or social surplus. We show that efficiency cost of prizes is a key consideration. Races are undesirable only when efficiency costs are low, firms are similar, and social surplus is maximized. Otherwise, the optimal policy involves a race of nontrivial duration to spur innovation and filter out inferior innovators.

We study North–South capital transfer and the diffusion of embodied technologies within a framework of intertemporal global welfare maximization. We show saddle path stability and characterize the steady state. We then examine the transition path by running numerical experiments based on realistic data. As a result, technology diffusion will succeed if the absorptive capacity is sufficient which requires sufficient investment. While a large share of capital is allocated to the South in early periods, this share declines in later periods when the South has caught up in terms of technologies.

We investigate the socially optimal intervention in the global carbon cycle. Limiting factors are (i) increasing atmospheric carbon concentration due to fossil fuel-related carbon emissions, and (ii) the inertia of the global carbon cycle itself. Accordingly, we explicitly include the largest non-atmospheric carbon reservoir, the ocean, to achieve a better representation of the global carbon cycle than the proportional-decay assumption usually resorted to in economic models. We also investigate the option to directly inject CO2 into the deep ocean (a form of carbon sequestration), deriving from this a critical level for ocean sequestration costs. Above this level, ocean sequestration is merely a temporary option; below it, ocean sequestration is the long-term option permitting extended use of fossil fuels. The latter alternative involves higher atmospheric stabilization levels. In this connection it should be noted that the efficiency of ocean sequestration depends on the time-preference and the inertia of the carbon cycle.

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We present a new way to solve principal agent problems by polynomial programming techniques. We study the case where the agent's actions are unobservable by the principal but the outcomes are. We assume that the agent's actions lie in an interval and the space of outcomes is a finite set. Furthermore the agent's expected utility is a rational function in his actions. The resulting problem is a bilevel optimization problem with the principal's problem as the upper and the agent's problem as the lower level. The key idea is to find an exact reformulation of the agent's problem as a semidefinite optimization problem. Since this is a convex optimization problem, we then have necessary and sufficient global optimality conditions for the agent's problem. The reformulation can be done by using classical results from real algebraic geometry linking positive polynomials and semidefinite matrices. We obtain a nonlinear program. If all functions are rational functions, we then can solve it to global optimality.

We present a new way to solve principal agent problems by polynomial programming techniques. We study the case where the agent's actions are unobservable by the principal but the outcomes are. We assume that the agent's actions lie in an interval and the space of outcomes is a finite set. Furthermore the agent's expected utility is a rational function in his actions. The resulting problem is a bilevel optimization problem with the principal's problem as the upper and the agent's problem as the lower level. The key idea is to find an exact reformulation of the agent's problem as a semidefinite optimization problem. Since this is a convex optimization problem, we then have necessary and sufficient global optimality conditions for the agent's problem. The reformulation can be done by using classical results from real algebraic geometry linking positive polynomials and semidefinite matrices. We obtain a nonlinear program. If all functions are rational functions, we then can solve it to global optimality.