Risk and Decision Analysis - Volume 3, issue 3

Article Type: Other

DOI: 10.3233/RDA-2011-0056

Citation: Risk and Decision Analysis, vol. 3, no. 3, pp. 147-147, 2012

Authors: Ledvina, Andrew | Sircar, Ronnie

Article Type: Research Article

Abstract: We study continuous time oligopolies in which a small number of firms producing similar goods compete with one another by setting prices or quantities. We study a deterministic version of the problem using an asymptotic expansion of the relevant HJB partial differential equations. We find in this setting that for firms with highly differentiated goods, the type of competition matters little. For less differentiated goods, we find that the Cournot type market produces a greater value to the firms than the Bertrand type market. We then study a stochastic version of the two games using numerical techniques. This allows us …to compare firms with a greater degree of product differentiation. The value is still greater to firms in most scenarios in a Cournot market, but in some situations the classical Bertrand–Cournot dichotomy is reversed. Show more

Keywords: Differential games, oligopoly, product differentiation, asymptotic expansion

DOI: 10.3233/RDA-2011-0057

Citation: Risk and Decision Analysis, vol. 3, no. 3, pp. 149-165, 2012

Authors: Tang, Shanjian | Wei, Wenning

Article Type: Research Article

Abstract: For the natural filtration generated by a Brownian motion and a Poisson random measure, the representation of the generator of backward stochastic differential equations and a converse comparison theorem are proved. Moreover, the relation is discussed between g-expectations and dynamic convex and coherent risk measures. The integral representation is discussed for the minimal penalty term of a dynamic convex risk measure.

Keywords: Dynamic convex risk measure, dynamic coherent risk measure, Poisson random measure, backward stochastic differential equations, g-expectation, minimal penalty term, conjugate function

DOI: 10.3233/RDA-2011-0060

Citation: Risk and Decision Analysis, vol. 3, no. 3, pp. 167-190, 2012

Authors: Nagai, Hideo

Article Type: Research Article

Abstract: We are interested in exploring methodology to estimate small probabilities of rare events from the view points of stochastic control. In particular, we study portfolio choice to be selected by an investor possessing several kinds of securities under prescribed consumption level, who is considering minimizing down-side risk probability for his (her) total wealth of falling below a given target growth rate in the long term. We shall show the problem finding the strategy minimizing such probability is considered large deviations control. From this viewpoint we shall state about general asymptotic theory for factor models, explicit calculation for linear Gaussian models, …and consideration in the case of complete market models. Show more

Keywords: Large deviation, long-term investment and consumption, risk-sensitive stochastic control, H–J–B equation of ergodic type

DOI: 10.3233/RDA-2011-0058

Citation: Risk and Decision Analysis, vol. 3, no. 3, pp. 191-200, 2012

Authors: Privault, Nicolas | Teng, Timothy Robin

Article Type: Research Article

Abstract: In this paper we review the hedging of interest rate derivatives priced under the risk-neutral measure, and we compute self-financing hedging strategies for various derivatives using the Clark–Ocone formula.

Keywords: Bond markets, hedging, infinite-dimensional analysis, Clark–Ocone formula, swaptions, bond options, caplets

DOI: 10.3233/RDA-2011-0061

Citation: Risk and Decision Analysis, vol. 3, no. 3, pp. 201-209, 2012

Authors: Kaise, Hidehiro | Sekine, Jun

Article Type: Research Article

Abstract: Risk-sensitive portfolio optimization is treated with a linear-Gaussian-factor model. The main interest is how a highly risk-averse investor controls his/her interest rate risk. A simple risk-averse limit with increasing risk-averse parameter γ↑∞ is not appropriate: the associated maximized risk-sensitized expected growth rate goes to −∞ as γ↑∞, and a “breakdown” occurs in the limit. Instead, a small-noise and large-risk-aversion limit is considered, assuming the factor-noise has a small parameter ε<<1, taking ε-dependent risk-averse parameter γ(ε)=O(ε−2 )>>1, and letting ε↓0. The limit value is characterized as the value of a linear-quadratic differential game. A sequence (π˜ (ε))ε>0 of ε-dependent dynamic …investment strategies is constructed from a saddle point of the game, and its asymptotic optimality is shown as ε↓0. Show more

Keywords: Risk-sensitive portfolio optimization, small-factor-noise, large-risk-aversion, linear quadratic differential game, saddle point, asymptotically optimal strategy, fund separation theorem, hedging-demand-term

DOI: 10.3233/RDA-2011-0059

Citation: Risk and Decision Analysis, vol. 3, no. 3, pp. 211-222, 2012