Dynamic exponential utility indifference valuation

We study the dynamics of the exponential utility indifference value process C(B;\alpha) for a contingent claim B in a semimartingale model with a general continuous filtration. We prove that C(B;\alpha) is (the first component of) the unique solution of a backward stochastic differential equation with a quadratic generator and obtain BMO estimates for the components of this solution. This allows us to prove several new results about C_t(B;\alpha). We obtain continuity in B and local Lipschitz-continuity in the risk aversion \alpha, uniformly in t, and we extend earlier results on the asymptotic behavior as \alpha\searrow0 or \alpha\nearrow\infty to our general setting. Moreover, we also prove convergence of the corresponding hedging strategies.Comment: Published at http://dx.doi.org/10.1214/105051605000000395 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

THE VALUE OF THE VIEW: VALUING SCENIC QUALITY USING CHOICE AND CONTINGENT VALUATION MODELS

Scenic beauty contributes to residents' quality of life and also serves to attract visitors to recreational areas. Because of the dynamic relationship between people, land, and rural development, there is an increasing interest in estimating the value of scenic quality using nonmarket valuation techniques. This study estimates the value of scenic quality to Blue Ridge Parkway visitors using choice and contingent valuation models. Results suggest that further research into respondent perceptions of CM and CVM models, and the conditions under which they yield comparable estimates, is warranted.Institutional and Behavioral Economics,

A Dual Method For Backward Stochastic Differential Equations with Application to Risk Valuation

We propose a numerical recipe for risk evaluation defined by a backward stochastic differential equation. Using dual representation of the risk measure, we convert the risk valuation to a stochastic control problem where the control is a certain Radon-Nikodym derivative process. By exploring the maximum principle, we show that a piecewise-constant dual control provides a good approximation on a short interval. A dynamic programming algorithm extends the approximation to a finite time horizon. Finally, we illustrate the application of the procedure to financial risk management in conjunction with nested simulation and on an multidimensional portfolio valuation problem

Some numerical methods for solving stochastic impulse control in natural gas storage facilities

The valuation of gas storage facilities is characterized as a stochastic impulse control problem with finite horizon resulting in Hamilton-Jacobi-Bellman (HJB) equations for the value function. In this context the two catagories of solving schemes for optimal switching are discussed in a stochastic control framework. We reviewed some numerical methods which include approaches related to partial differential equations (PDEs), Markov chain approximation, nonparametric regression, quantization method and some practitioners’ methods. This paper considers optimal switching problem arising in valuation of gas storage contracts for leasing the storage facilities, and investigates the recent developments as well as their advantages and disadvantages of each scheme based on dynamic programming principle (DPP

An information approach to the dynamics in farm income: implications for farmland markets

The valuation of farmland is a perennial issue for agricultural policy, given its importance in the farm investment portfolio. Despite the significance of farmland values to farmer wealth, prediction remains a difficult task. This study develops a dynamic information measure to examine the informational content of farmland values and farm income in explaining the distribution of farmland values over time

Dynamic State Tameness

An extension of the idea of state tameness is presented in a dynamic framework. The proposed model for financial markets is rich enough to provide analytical tools that are mostly obtained in models that arise as the solution of SDEs with deterministic coefficients. In the presented model the augmentation by a shadow stock of the price evolution has a Markovian character. As in a previous paper, the results obtained on valuation of European contingent claims and American contingent claims do not require the full range of the volatility matrix. Under some additional continuity conditions, the conceptual framework provided by the model makes it possible to regard the valuation of financial instruments of the European type as a particular case of valuation of instruments of American type. This provides a unifying framework for the problem of valuation of financial instruments.arbitrage; pricing of contingent claims; continuous-time financial markets; tameness; stochastic flows.

Dynamic Willingness to Pay: An Empirical Specification and Test

In a static setting, willingness to pay for an environmental improvement is equal to compensating variation. However, in a dynamic setting characterized by uncertainty, irreversibility, and the potential for learning, willingness to pay may also contain an option value. In this paper, we incorporate the dynamic nature of the value formulation process into a study using a contingent valuation method, designed to measure the value local residents assign to a north-central Iowa lake. Our results show that willingness to pay is highly sensitive to the potential for future learning. Respondents offered the opportunity to delay their purchasing decisions until more information became available were willing to pay significantly less for improved water quality than those who faced a now-or-never decision. The results suggest that welfare analysts should take care to accurately represent the potential for future learning.Clear Lake, contingent valuation, water quality, willingness to pay.