Ethem Çanakoğlu

Portfolio selection in stochastic markets with HARA utility functions

In this paper, we consider the optimal portfolio selection problem where the investor maximizes the expected utility of the terminal wealth. The utility function belongs to the HARA family which includes exponential, logarithmic, and power utility functions. The main feature of the model is that returns of the risky assets and the utility function all depend on an external process that represents the stochastic market. The states of the market describe the prevailing economic, financial, social, political and other conditions that affect the deterministic and probabilistic parameters of the model. We suppose that the random changes in the market states are depicted by a Markov chain. Dynamic programming is used to obtain an explicit characterization of the optimal policy. In particular, it is shown that optimal portfolios satisfy the separation property and the composition of the risky portfolio does not depend on the wealth of the investor. We also provide an explicit construction of the optimal wealth process and use it to determine various quantities of interest. The return-risk frontiers of the terminal wealth are shown to have linear forms. Special cases are discussed together with numerical illustrations.

Robust strategies for facility location under uncertainty

This paper considers a stochastic facility location problem in which multiple capacitated facilities serve customers with a single product, and a stockout probabilistic requirement is stated as a chance constraint. Customer demand is assumed to be uncertain and to follow either a normal or an ambiguous distribution. We study robust approximations to the problem in order to incorporate information about the random demand distribution in the best possible, computationally tractable way. We also discuss how a decision maker’s risk preferences can be incorporated in the problem through robust optimization. Finally, we present numerical experiments that illustrate the performance of the different robust formulations. Robust optimization strategies for facility location appear to have better worst-case performance than nonrobust strategies. They also outperform nonrobust strategies in terms of realized average total cost when the actual demand distributions have higher expected values than the expected values used as input to the optimization models.

Portfolio selection in stochastic markets with exponential utility functions

We consider the optimal portfolio selection problem in a multiple period setting where the investor maximizes the expected utility of the terminal wealth in a stochastic market. The utility function has an exponential structure and the market states change according to a Markov chain. The states of the market describe the prevailing economic, financial, social and other conditions that affect the deterministic and probabilistic parameters of the model. This includes the distributions of the random asset returns as well as the utility function. The problem is solved using the dynamic programming approach to obtain the optimal solution and an explicit characterization of the optimal policy. We also discuss the stochastic structure of the wealth process under the optimal policy and determine various quantities of interest including its Fourier transform. The exponential return-risk frontier of the terminal wealth is shown to have a linear form. Special cases of multivariate normal and exponential returns are disussed together with a numerical illustration.

HARA frontiers of optimal portfolios in stochastic markets

Abstract In this paper, we consider the optimal portfolio selection problem in continuous-time settings where the investor maximizes the expected utility of the terminal wealth in a stochastic market. The utility function has the structure of the HARA family and the market states change according to a Markov process. The states of the market describe the prevailing economic, financial, social and other conditions that affect the deterministic and probabilistic parameters of the model. This includes the distributions of the random asset returns as well as the utility function. We analyzed Black–Scholes type continuous-time models where the market parameters are driven by Markov processes. The Markov process that affects the state of the market is independent of the underlying Brownian motion that drives the stock prices. The problem of maximizing the expected utility of the terminal wealth is investigated and solved by stochastic optimal control methods for exponential, logarithmic and power utility functions. We found explicit solutions for optimal policy and the associated value functions. We also constructed the optimal wealth process explicitly and discussed some of its properties. In particular, it is shown that the optimal policy provides linear frontiers.

Analysis of a two-stage telecommunication supply chain with technology dependent demand

We analyze a two-stage telecommunication supply chain consisting of one operator and one vendor under a multiple period setting. The operator faces a stochastic market demand which depends on technology investment level. The decision variables for the operator are the initial technology investment level and the capacity of the network for each period. The capacity that the operator installs in one period also remains available in subsequent periods. The operator can increase or decrease the available capacity at each period. For this model, an algorithm to find the centralized optimal solution is proposed. A profit sharing contract where firms share both the revenue and operating costs generated throughout the periods along with initial technology investment is suggested. Also a coordinating quantity discount contract where the discount on the price depends on the total installed capacity is designed. The case where the vendor decides on the technology investment level and the operator decides on the capacity of the network is also analyzed and it is shown that this game has a unique Nash equilibrium.

Robust investment decisions under supply disruption in petroleum markets

Energy-dependent economies and energy security strategies need to cope with oil and gas supply disruptions that are rare but persistent and can be financially catastrophic. This paper proposes a tractable approach for determining robust investment strategies in petroleum markets under the risk of supply disruption when asset prices follow geometric mean-reverting jump processes. The robust counterpart of the portfolio management problem under supply disruption is derived for several symmetric and asymmetric representations of the uncertainties in the problem. Computational experiments with real market data indicate that the robust optimization approach using uncertainty sets tailored to the characteristics of the data results in strategies with superior worst-case performance.

Robust team decision-making under uncertainty

This paper is concerned with multi-agent team modelling and robust decision-making problems arising in mission planning under uncertainty. We consider multi-agent planning problem with task coordination using stochastic programming. Agents within a centralised team cooperate so that the expected team performance is maximised. The success of each agent to accomplish any task is critical for the team performance. Inaccuracy on estimation of uncertain success probability is addressed using robust optimisation where different uncertainty sets are considered. Robust optimisation computes the optimal task allocation simultaneously with worst-case by taking into account of all scenarios. The computational results show trade-off between team efficiency and robustness of solution.

Heuristics for the stochastic dynamic task-resource allocation problem with retry opportunities

This paper deals with a stochastic multi-period task-resource allocation problem. A team of agents with a set of resources is to be deployed on a multi-period mission with the goal to successfully complete as many tasks as possible. The success probability of an agent assigned to a task depends on the resources available to the agent. Unsuccessful tasks can be tried again at later periods. While the problem can in principle be solved by dynamic programming, in practice this is computationally prohibitive except for tiny problem sizes. To be able to tackle also larger problems, we propose a construction heuristic that assigns agents and resources to tasks sequentially, based on the estimated marginal utility. Based on this heuristic, we furthermore propose various Approximate Dynamic Programming approaches and an Evolutionary Algorithm. All suggested approaches are empirically compared on a number of randomly generated problem instances. We show that the construction heuristic is very fast and provides good results. For even better results, at the expense of longer computational time, Approximate Dynamic Programming seems a suitable alternative.

A robust asset---liability management framework for investment products with guarantees

This paper suggests a robust asset–liability management framework for investment products with guarantees, such as guaranteed investment contracts and equity-linked notes. Stochastic programming and robust optimization approaches are introduced to deal with data uncertainty in asset returns and interest rates. The statistical properties of the probability distributions of uncertain parameters are incorporated in the model through appropriately selected symmetric and asymmetric uncertainty sets. Practical data-driven approaches for implementation of the robust models are also discussed. Numerical results using generated and real market data are presented to illustrate the performance of the robust asset–liability management strategies. The robust investment strategies show better performance in unfavorable market regimes than traditional stochastic programming approaches. The effectiveness of robust investment strategies can be improved by calibrating carefully the shape and the size of the uncertainty sets for asset returns.

Modeling of carbon credit prices using regime switching approach

In this study, we analyze the price dynamics of carbon certificates that are traded under the European Unions Emissions Trading System (EU-ETS). With the aim of investigating the joint relations among carbon, electricity, and fuel prices, we model historical prices using several methods and incorporating structural changes, such as econometric time series, regime switching, and multivariate vector autoregression models. We compare the results of the structural model with the results of traditional Markov switching and autoregressive models with breaks and present performance analysis based on the mean average percentage error, root mean squared error, and coefficient of determination. According to these performance tests, models with regimes outperform the approaches where breaks are defined using ex ante dummy variables. Moreover, we conclude that among regime switching models, univariate models are better than multivariate counterparts for modeling carbon price series for the analysis of both in-sample and out-of-samples.In this study, we analyze the price dynamics of carbon certificates that are traded under the European Unions Emissions Trading System (EU-ETS). With the aim of investigating the joint relations among carbon, electricity, and fuel prices, we model historical prices using several methods and incorporating structural changes, such as econometric time series, regime switching, and multivariate vector autoregression models. We compare the results of the structural model with the results of traditional Markov switching and autoregressive models with breaks and present performance analysis based on the mean average percentage error, root mean squared error, and coefficient of determination. According to these performance tests, models with regimes outperform the approaches where breaks are defined using ex ante dummy variables. Moreover, we conclude that among regime switching models, univariate models are better than multivariate counterparts for modeling carbon price series for the analysis of both in-sample...