Mathematical Finance
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Return Dynamics when Persistence is UnobservableThis paper proposes a new theory of the sources of time‐varying second (and higher) moments in financial time series. The key idea is that fully rational agents must infer the stochastic degree of persistence of fundamental shocks. Endogenous changes in their uncertainty determine the evolution of conditional moments of returns. The model accounts for the principal observed features of vol... ... hiện toàn bộ
Mathematical Finance - Tập 11 Số 4 - Trang 415-445 - 2001
Static hedging and pricing of exotic options with payoff framesAbstract We develop a general framework for statically hedging and pricing European‐style options with nonstandard terminal payoffs, which can be applied to mixed static–dynamic and semistatic hedges for many path‐dependent exotic options including variance swaps and barrier options. The goal is achieved by separating the hedging and pricing problems to obtain repli... ... hiện toàn bộ
Mathematical Finance - Tập 29 Số 2 - Trang 612-658 - 2019
BEHAVIORAL PORTFOLIO SELECTION IN CONTINUOUS TIMEThis paper formulates and studies a general continuous‐time behavioral portfolio selection model under Kahneman and Tversky's (cumulative) prospect theory, featuring S‐shaped utility (value) functions and probability distortions. Unlike the conventional expected utility maximization model, such a behavioral model could be easily mis‐formulated (a.k.a. ill‐posed) if its different components... ... hiện toàn bộ
Mathematical Finance - Tập 18 Số 3 - Trang 385-426 - 2008
OPTIMAL INSURANCE DESIGN UNDER RANK‐DEPENDENT EXPECTED UTILITYWe consider an optimal insurance design problem for an individual whose preferences are dictated by the rank‐dependent expected utility (RDEU) theory with a concave utility function and an inverse‐S shaped probability distortion function. This type of RDEU is known to describe human behavior better than the classical expected utility. By applying the technique of quantile formulation, we s... ... hiện toàn bộ
Mathematical Finance - Tập 25 Số 1 - Trang 154-186 - 2015
TRACTABLE ROBUST EXPECTED UTILITY AND RISK MODELS FOR PORTFOLIO OPTIMIZATION
Mathematical Finance - Tập 20 Số 4 - Trang 695-731
Explicit Representation of the Minimal Variance Portfolio in Markets Driven by Lévy ProcessesIn a market driven by a Lévy martingale, we consider a claim ξ. We study the problem of minimal variance hedging and we give an explicit formula for the minimal variance portfolio in terms of Malliavin derivatives. We discuss two types of stochastic (Malliavin) derivatives for ξ: one based on the chaos expansion in terms of iterated integrals with respect to the power jump processes and on... ... hiện toàn bộ
Mathematical Finance - Tập 13 Số 1 - Trang 55-72 - 2003
A DIFFUSION MODEL FOR ELECTRICITY PRICESStarting from a simple supply/demand model for electricity, we obtain a diffusion (i.e., jumpless) model for spot prices which can exhibit price spikes. We estimate the parameters in the model using historical data from the Alberta and California markets. and compare this model with some others used for spot prices.
Mathematical Finance - Tập 12 Số 4 - Trang 287-298 - 2002
Coherent Measures of RiskIn this paper we study both market risks and nonmarket risks, without complete markets assumption, and discuss methods of measurement of these risks. We present and justify a set of four desirable properties for measures of risk, and call the measures satisfying these properties “coherent.” We examine the measures of risk provided and the related actions required by SPAN, by the SEC/NASD r... ... hiện toàn bộ
Mathematical Finance - Tập 9 Số 3 - Trang 203-228 - 1999
Unspanned stochastic volatility in the multifactor CIR modelAbstract Empirical evidence suggests that fixed‐income markets exhibit unspanned stochastic volatility (USV), that is, that one cannot fully hedge volatility risk solely using a portfolio of bonds. While Collin‐Dufresne and Goldstein (2002, Journal of Finance , 57 , 1685–1730) showed that no two‐factor Cox–Ingersol... ... hiện toàn bộ
Mathematical Finance - Tập 29 Số 3 - Trang 827-836 - 2019
Complete Models with Stochastic VolatilityThe paper proposes an original class of models for the continuous‐time price process of a financial security with nonconstant volatility. The idea is to define instantaneous volatility in terms of exponentially weighted moments of historic log‐price. The instantaneous volatility is therefore driven by the same stochastic factors as the price process, so that, unlike many other models of no... ... hiện toàn bộ
Mathematical Finance - Tập 8 Số 1 - Trang 27-48 - 1998
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