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 Quantitative Finance , 2011, Abstract: A key issue in the estimation of energy hedges is the hedgers' attitude towards risk which is encapsulated in the form of the hedgers' utility function. However, the literature typically uses only one form of utility function such as the quadratic when estimating hedges. This paper addresses this issue by estimating and applying energy market based risk aversion to commonly applied utility functions including log, exponential and quadratic, and we incorporate these in our hedging frameworks. We find significant differences in the optimal hedge strategies based on the utility function chosen.
 Mathematics , 2009, Abstract: Kramkov and Sirbu (2006, 2007) have shown that first-order approximations of power utility-based prices and hedging strategies can be computed by solving a mean-variance hedging problem under a specific equivalent martingale measure and relative to a suitable numeraire. In order to avoid the introduction of an additional state variable necessitated by the change of numeraire, we propose an alternative representation in terms of the original numeraire. More specifically, we characterize the relevant quantities using semimartingale characteristics similarly as in Cerny and Kallsen (2007) for mean-variance hedging. These results are illustrated by applying them to exponential L\'evy processes and stochastic volatility models of Barndorff-Nielsen and Shephard type.
 Dirk Becherer Mathematics , 2007, DOI: 10.1214/105051606000000475 Abstract: We prove results on bounded solutions to backward stochastic equations driven by random measures. Those bounded BSDE solutions are then applied to solve different stochastic optimization problems with exponential utility in models where the underlying filtration is noncontinuous. This includes results on portfolio optimization under an additional liability and on dynamic utility indifference valuation and partial hedging in incomplete financial markets which are exposed to risk from unpredictable events. In particular, we characterize the limiting behavior of the utility indifference hedging strategy and of the indifference value process for vanishing risk aversion.
 Yun-Yeong Kim Theoretical Economics Letters (TEL) , 2013, DOI: 10.4236/tel.2013.31001 Abstract: This paper introduces the optimal foreign exchange risk hedging model following a standard portfolio theory. The results indicate that a lower level of risk can be achieved, given a specified level of expected return, from using optimization modeling. In the paper the expected hedging return is defined from the expected cost of the foreign currency using a specified hedging strategy minus the expected cost of the foreign currency when it is purchased form the spot market. The focal point of the technique is its ability to identify optimal combinations of hedging vehicles, those are currency options, forward contracts, leaving the position open (foreign exchange risk hedging tools suggested by the US. Department of Commerce) in a closed form.
 Journal of Mathematical Finance (JMF) , 2016, DOI: 10.4236/jmf.2016.63036 Abstract: Within the optimal production and hedging decision framework, Lien compares the exponential utility function with its second order approximation under the normality distribution assumption. In this paper, we first extend the result further by comparing the exponential utility function with a 2n-order approximation for any integer n. We then propose an approach with illustration to find the smallest n that provides a good approximation.
 Mathematics , 2012, Abstract: In this note, we explicitly solve the problem of maximizing utility of consumption (until the minimum of bankruptcy and the time of death) with a constraint on the probability of lifetime ruin, which can be interpreted as a risk measure on the whole path of the wealth process.
 Jochen Zahn Quantitative Finance , 2011, DOI: 10.1142/S0219024912500525 Abstract: We discuss utility based pricing and hedging of jump diffusion processes with emphasis on the practical applicability of the framework. We point out two difficulties that seem to limit this applicability, namely drift dependence and essential risk aversion independence. We suggest to solve these by a re-interpretation of the framework. This leads to the notion of an implied drift. We also present a heuristic derivation of the marginal indifference price and the marginal optimal hedge that might be useful in numerical computations.
 Mathematics , 2011, Abstract: A function $u: X\to\mathbb{R}$ defined on a partially ordered set is quasi-Leontief if, if for all $x\in X$, the upper level set $\{x^\prime\in X: u(x^\prime)\geqslant u(x)\}$ has a smallest element. A function $u: \prod_{j=1}^nX_j\to\mathbb{R}$ whose partial functions obtained by freezing $n-1$ of the variables are all quasi-Leontief is an individually quasi-Leontief function; a point $x$ of the product space is an efficient point for $u$ if it is a minimal element of $\{x^\prime\in X: u(x^\prime)\geqslant u(x)\}$. Part I deals with the maximisation of quasi-Leontief functions and the existence of efficient maximizers. Part II is concerned with the existence of efficient Nash equilibria for abstract games whose payoff functions are individually quasi-Leontief. Order theoretical and algebraic arguments are dominant in the first part while, in the second part, topology is heavily involved. In the framework and the language of tropical algebras, our quasi-Leontief functions are the additive functions defined on a semimodule with values in the semiring of scalars.
 Computer Science , 2010, Abstract: We study the stochastic versions of a broad class of combinatorial problems where the weights of the elements in the input dataset are uncertain. The class of problems that we study includes shortest paths, minimum weight spanning trees, and minimum weight matchings over probabilistic graphs, and other combinatorial problems like knapsack. We observe that the expected value is inadequate in capturing different types of {\em risk-averse} or {\em risk-prone} behaviors, and instead we consider a more general objective which is to maximize the {\em expected utility} of the solution for some given utility function, rather than the expected weight (expected weight becomes a special case). We show that we can obtain a polynomial time approximation algorithm with {\em additive error} $\epsilon$ for any $\epsilon>0$, if there is a pseudopolynomial time algorithm for the {\em exact} version of the problem (This is true for the problems mentioned above) and the maximum value of the utility function is bounded by a constant. Our result generalizes several prior results on stochastic shortest path, stochastic spanning tree, and stochastic knapsack. Our algorithm for utility maximization makes use of the separability of exponential utility and a technique to decompose a general utility function into exponential utility functions, which may be useful in other stochastic optimization problems.
 Spanò Marcello Panoeconomicus , 2013, DOI: 10.2298/pan1302203s Abstract: Emerging markets in the last decade increased the stock of foreign reserves and simultaneously managed to raise GDP growth while leaving short term foreign debt and investment in net fixed capital nearly unchanged. This work builds a model able to derive these facts as the result of greater openness to global goods and financial markets. Emerging countries generate the observed high ratios of reserves to short term foreign debt to hedge against volatility of foreign capital inflow with the purpose of stabilising not the short term but the long term finance available to domestic firms. Numerical simulations of the model derive the rising level of reserves to short term foreign debt ratio and about half of the observed rise in GDP growth as a result of a falling cost of long term finance and the increasing competitiveness of domestic industry.
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