1,720,967 research outputs found
Viscosity Characterization of the Value Function of an Investment-Consumption Problem in Presence of an Illiquid Asset
Full text linkWe study a problem of optimal investment/consumption over an infinite horizon in a market consisting of a liquid and an illiquid asset. The liquid asset is observed and can be traded continuously, while the illiquid one can only be traded and observed at discrete random times corresponding to the jumps of a Poisson process. The problem is a nonstandard mixed discrete/continuous optimal control problem, which we face by the dynamic programming approach. The main goal of the paper is the characterization of the value function as unique viscosity solution of an associated Hamilton-Jacobi-Bellman equation. We then use such a result to build a numerical algorithm, allowing one to approximate the value function and so to measure the cost of illiquidity. © 2013 Springer Science+Business Media New York
Impact of time illiquidity in a mixed market without full observation
Full text linkWe study a problem of optimal investment/consumption over an infinite horizon in a market with two possibly correlated assets: one liquid and one illiquid. The liquid asset is observed and can be traded continuously, while the illiquid one can be traded only at discrete random times, corresponding to the jumps of a Poisson process with intensity λ, is observed at the trading dates, and is partially observed between two different trading dates. The problem is a nonstandard mixed discrete/continuous optimal control problem, which we solve by a dynamic programming approach. When the utility has a general form, we prove that the value function is the unique viscosity solution of the associated Hamilton–Jacobi–Bellman equation and characterize the optimal allocation in the illiquid asset. In the case of power utility, we establish the regularity of the value function needed to prove the verification theorem, providing the complete theoretical solution of the problem. This enables us to perform numerical simulations, so as to analyze the impact of time illiquidity and how this impact is affected by the degree of observation
Dynamic Programming for an Investment/Consumption problem in illiquid markets with regime-switching
No full textShort-dated smile under rough volatility: asymptotics and numerics
No full textIn Friz et al. [Precise asymptotics for robust stochastic volatility models. Ann. Appl. Probab, 2021, 31(2), 896-940], we introduce a new methodology to analyze large classes of (classical and rough) stochastic volatility models, with special regard to short-time and small-noise formulae for option prices, using the framework [Bayer et al., A regularity structure for rough volatility. Math. Finance, 2020, 30(3), 782-832]. We investigate here the fine structure of this expansion in large deviations and moderate deviations regimes, together with consequences for implied volatility. We discuss computational aspects relevant for the practical application of these formulas. We specialize such expansions to prototypical rough volatility examples and discuss numerical evidence
Precise asymptotics: Robust stochastic volatility models
No full textWe present a new methodology to analyze large classes of (classical and rough) stochastic volatility models, with special regard to short-time and small noise formulae for option prices. Our main tool is the theory of regularity structures, which we use in the form of Bayer et al. (Math. Finance 30 (2020) 782-832) In essence, we implement a Laplace method on the space of models (in the sense of Hairer), which generalizes classical works of Azencott and Ben Arous on path space and then Aida, Inahama-Kawabi on rough path space. When applied to rough volatility models, for example, in the setting of Bayer, Friz and Gatheral (Quant. Finance 16 (2016) 887-904) and Forde-Zhang (SIAM J. Financial Math. 8 (2017) 114-145), one obtains precise asymptotics for European options which refine known large deviation asymptotics
Utility maximization with current utility on the wealth: regularity of solutions to the HJB equation
Full text linkThis paper deals with an investment–consumption portfolio problem when the current utility depends also on the wealth process. Such problems arise e.g. in portfolio optimization with random horizon or random trading times. To overcome the difficulties of the problem, a dual approach is employed: a dual control problem is defined and treated by means of dynamic programming, showing that the viscosity solutions of the associated Hamilton–Jacobi–Bellman equation belong to a suitable class of smooth functions. This allows defining a smooth solution of the primal Hamilton–Jacobi–Bellman equation, and proving by verification that such a solution is indeed unique in a suitable class of smooth functions and coincides with the value function of the primal problem. Applications to specific financial problems are given. © 2015, Springer-Verlag Berlin Heidelberg
Regularization by noise for stochastic Hamilton-Jacobi equations
No full textGassiat P, Gess B. Regularization by noise for stochastic Hamilton-Jacobi equations. PROBABILITY THEORY AND RELATED FIELDS. 2019;173(3-4):1063-1098.We study regularizing effects of nonlinear stochastic perturbations for fully nonlinear PDE. More precisely, path-by-path L bounds for the second derivative of solutions to such PDE are shown. These bounds are expressed as solutions to reflected SDE and are shown to be optimal
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Variations on the Author
Full text link“Variations on the Author” discusses two of Eduardo Coutinho’s recent films (Um Dia na Vida, from 2010, and Últimas Conversas, posthumously released in 2015) and their contribution to the general question of documentary authorship. The director’s filmography is characterized by a consistent yet self-effacing form of authorial self-inscription: Coutinho often features as an interviewer that rather than express opinions propels discourses; an interviewer that is good at listening. This mode of self-inscription characterizes him as an author who is not expressive but who is nonetheless markedly present on the screen. In Um Dia na Vida, however, Coutinho is completely absent form the image, while Últimas Conversas, on the contrary, includes a confessional prologue that moves the director from the margins to the center of his films. This article examines the ways in which these works stand out in the filmography of a director who offers new insights into the notion of cinematic authorship
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