Continuous-time mean-variance portfolio optimization in a jump-diffusion market

In this paper, we take up an approach of (Lindberg, in Bernoulli, 15(2):464–474, 2009) who introduced a new parameterization of the Black–Scholes model that allows for an easy solution of the continuous-time Markowitz mean-variance problem. We generalize the results of (Lindberg, in Bernoulli, 15(2):464–474, 2009) to a jump-diffusion market setting and slightly correct the proof and the assertion of the main result. Further, we demonstrate the implications of the Lindberg parameterization for the stock price drift vector in different market settings, analyse the dependence of the optimal portfolio from jump and diffusion risk and finally indicate how to use the method. We particularly also show how the optimal strategy can be obtained with the restricted use of historical data.     

Consumption paths under prospect utility in an optimal growth model

This paper studies the Cass-Koopmans-Ramsey model of optimal economic growth in the presence of loss aversion and habit formation. The representative agent's preferences for consumption can be gradually varied between the standard constant intertemporal elasticity of substitution (CIES) case and Kahneman and Tversky's prospect utility. We find that the transitional dynamics of optimal consumption paths differ distinctly from the standard model, in particular consumption smoothing is more pronounced. We also show that prospect utility can cause the economy to remain in a steady state with low consumption and low capital.     

Computation of Greeks using binomial trees in a jump-diffusion model

We propose a new algorithm for computing the Greeks in jump-diffusion settings using binomial trees. We further demonstrate that the Greeks for European options converge to the Malliavin Greeks in the continuous time model. Our proposed algorithm is efficient, because the price and the Greeks (Delta, Gamma, Vega, and Rho) can be computed simultaneously. Computation of the Greeks for American options is also discussed.     

Intertemporal recursive utility and an equilibrium asset pricing model in the presence of Lévy jumps

This paper presents an equilibrium formulation of asset pricing in an environment of mixed Poisson–Brownian information with recursive utility. The optimal portfolio choice problem is studied together with a derivation of Euler equation as necessary condition for optimality. It is further shown that the price processes governed by the Euler equation, together with the market clearing conditions, constitute the equilibrium price processes. Closed form formulas are derived for European call options and for other derivative securities in a particular parameterization of the economy. The derived option pricing formula contain many existing models as special cases, and is potentially useful in explaining the moneyness biasedness associated with Black–Scholes model.     

Consistent pricing of VIX options with the Hawkes jump-diffusion model

This paper presents a valuation of VIX options employing a Hawkes jump-diffusion model that captures the clustering pattern of jumps observed extensively in the financial markets. In the consistent framework, the valuation problem of VIX options is solved efficiently via the Fourier cosine expansion (COS) method. The Monte Carlo (MC) simulations are carried out to demonstrate the reliability and efficiency of the COS method. Furthermore, a sensitivity analysis is performed to show how option prices response to different parameters associated with jump clustering. Finally, empirical studies are conducted to provide evidence to support our jump specification in matching the VIX option surface.     

Density approximations for multivariate affine jump-diffusion processes

We introduce closed-form transition density expansions for multivariate affine jump-diffusion processes. The expansions rely on a general approximation theory which we develop in weighted Hilbert spaces for random variables which possess all polynomial moments. We establish parametric conditions which guarantee existence and differentiability of transition densities of affine models and show how they naturally fit into the approximation framework. Empirical applications in option pricing, credit risk, and likelihood inference highlight the usefulness of our expansions. The approximations are extremely fast to evaluate, and they perform very accurately and numerically stable.     

An existence theorem of intertemporal recursive utility in the presence of Lévy jumps

This paper presents an existence theorem for a class of backward stochastic integral equations. The main contribution is a generalization of Duffie and Epstein's [Duffie, D., Epstein, L., 1992. Stochastic differential utility, (Appendix C with Skiadas C.), Econometrica 60, 353–394.] existence theorem of intertemporal recursive utility to allow the information structure to be driven by a Lévy jump process. The existence theorem applies also for a more general class of utility functions, such as recursive utility with habit-formation, and can be used to prove the existence of an equilibrium asset price process as a unique solution to the stochastic Euler equation derived by Ma [Ma, C., 1993b. Valuation of Derivative Securities with Mixed Poisson–Brownian Information and Recursive Utility, McGill University, mimeo.].     

An iterative method for the computation of the correlation matrix implied by a recursive path model

Quality & Quantity - In Path Analysis, especially in social sciences studies, many researchers usually assume that errors in the model are uncorrelated with all exogenous variables as well as...     

Portfolio choice in the model of expected utility with a safety-first component

Decisions in Economics and Finance - The standard problem of portfolio choice between one risky and one riskless asset is analyzed in the model of expected utility with a safety-first component...     

Structural estimation of jump-diffusion processes in macroeconomics

This paper shows how to solve and estimate a continuous-time dynamic stochastic general equilibrium (DSGE) model with jumps. It also shows that a continuous-time formulation can make it simpler (relative to its discrete-time version) to compute and estimate the deep parameters using the likelihood function when non-linearities and/or non-normalities are considered. We illustrate our approach by solving and estimating the stochastic AK and the neoclassical growth models. Our Monte Carlo experiments demonstrate that non-normalities can be detected for this class of models. Moreover, we provide strong empirical evidence for jumps in aggregate US data.     

An optimization model for volunteer assignments in humanitarian organizations

One of the challenges facing humanitarian organizations is that there exist limited decision technologies that are tailored specifically to their needs. While employee workforce management models have been the topic of extensive research over the past decades, very little work has yet concentrated on the problem of managing volunteers for humanitarian organizations. This paper develops a multi-criteria optimization model to assist in the assignment of volunteers to tasks, based upon a series of principles from the field of volunteer management. In particular, it offers a new volunteer management approach for incorporating the decision maker's preferences and knowledge into the volunteer assignment process, thus allowing him or her to closely examine the tradeoffs between potentially conflicting objectives. Test results illustrate the model's ability to capture these tradeoffs and represent the imprecision inherent in the work of humanitarian organizations, and thus demonstrate its ability to support efficient and effective volunteer management.     

Consumption in the closed von Neumann model

Conclusion This new method for introducing extra consumption into the closed von Neumann model is not without flaw. In addition to requiring collusion by labor, the mechanism increases the dimension of the commodity space so that comparisons between intensity (or price) vectors before and after the introduction of consumption are difficult to make. It is claimed, however, that the method is free from the objection of Malinvaud. The method allows alternative processes for producing extra consumption and provides a mechanism for selecting among the alternative processes. Further, the new method solves the problem of allocating the extra consumption to the labor force.W. W. Cooper, Leif Johansen, and M. C. Lowell made helpful suggestions on earlier darfts of this article. This version is better for their help but any remaining errors are to be credited to my account.     

A set optimization approach to utility maximization under transaction costs

A set optimization approach to multi-utility maximization is presented, and duality results are obtained for discrete market models with proportional transaction costs. The novel approach allows us to obtain results for non-complete preferences, where the formulas derived closely resemble but generalize the scalar case.     

The dynamics of utility in the neoclassical OLG model

This paper develops a method to study how life-cycle utility of a sequence of cohorts converges to its steady state level in the neoclassical 2-period overlapping generations model. This method allows to characterize utility changes associated with marginal variations in exogenous policy parameters along the entire transition path between two steady states. At the same time, it is not more complicated than a pure steady state analysis. Moreover, it can be applied to economies for which an explicit solution of the transition path is not available.     

Tax rate uncertainty,labor supply and saving in a nonexpected utility maximizing model

The effects of uncertainty in rate of return tax rate, wage income tax rate and a comprehensive tax rate which affects both return to saving and wage income are analyzed in a nonexpected utility maximizing framework of Selden (1978). We consider a two period model where the agent works and saves. The effect of rate of return tax rate uncertainty on labor supply and saving critically depends on the magnitude of the elasticity of intertemporal substitution. A wage income tax rate uncertainty on the other hand unambiguously raises work effort while its effect on saving again depends on the magnitude of the intertemporal substitution elasticity. For empirically plausible magnitudes of the intertemporal substitution elasticity, saving responds positively to wage income tax rate risk. The effect of a comprehensive tax rate uncertainty on labor supply and saving, however, depends solely on the magnitude of the elasticity of intertemporal substitution.     

Planning in a public utility

This paper examines the pricing and allocation of electrical energy in the United States. Development planning for electrical energy is a continuous and sequential process involving mobilization and efficient use of resources over time and over space. Combining the temporal and spatial aspects of the problem, the concept of net social payoff is used as a basis for deducing the conditions of spatial and intertemporal equilibrium. The most important conclusion is that misallocation of electrical energy exists among consuming sectors. Because the price of electrical energy is too low for the industrial sector, the industrial sector is consuming a greater quantity than is optimal. Moreover, a better resource allocation would obtain if electrical energy development and operation were carried out by utilities on a national basis.     

A deep learning model for gas storage optimization

Decisions in Economics and Finance - To the best of our knowledge, the application of deep learning in the field of quantitative risk management is still a relatively recent phenomenon. In this...     

A recursive method for orthogonal designs

We introduce a class of arrays which can be used with amicable sets of matrices. Using a recursive method we introduce a class of amicable matrices which can be used in the new arrays to generate a large class of full orthogonal designs. The work was completed while the author was on study leave from University of Lethbridge, visiting IPM in Tehran. Hospitality and research grant provided by IPM is greatly appreciated. Supported by an NSERC Discovery grant     

Optimal investment of variance-swaps in jump-diffusion market with regime-switching

We consider a general jump-diffusion market with regime-switching where the jump risk is modeled as a Markov-modulated Poisson random measure. In this incomplete market, we price the variance-swaps using a combination of the Esscher transform and change of measure on time-inhomogeneous Markov chains. We study the dynamic optimal investment problem of the variance-swaps and characterize the optimal feedback strategy. Moreover, a closed-form solution to the HJB PDE associated with the stochastic control problem is established and the verification theorem is proved. The numerical analysis based on a two-state Markov chain uncovers some robust features of the optimal investment strategy.     

An optimization model for planning community health services.

This article reports results of a project to develop methods of planning health care delivery for a community with emphasis on ambulatory services in a health maintenance organization setting. Some of the special difficulties of the problem are discussed and a linear optimization model is presented that addresses the problem of planning the ambulatory service mix for a specified population. The model accounts for population characteristics, financial data, and system dynamics (including referral patterns). An application is shown for the case of a “model cities” population in Buffalo, New York, and some implications for further research are presented.