Mathematical Finance

SCOPUS (1991-2023)SCIE-ISI SSCI-ISI

  0960-1627

  1467-9965

  Anh Quốc

Cơ quản chủ quản:  WILEY , Wiley-Blackwell Publishing Ltd

Lĩnh vực:
Economics and EconometricsFinanceApplied MathematicsSocial Sciences (miscellaneous)Accounting

Các bài báo tiêu biểu

Coherent Measures of Risk
Tập 9 Số 3 - Trang 203-228 - 1999
Philippe Artzner, Freddy Delbaen, Jean‐Marc Eber, David Heath

In 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 rules, and by quantile‐based methods. We demonstrate the universality of scenario‐based methods for providing coherent measures. We offer suggestions concerning the SEC method. We also suggest a method to repair the failure of subadditivity of quantile‐based methods.

A YIELD‐FACTOR MODEL OF INTEREST RATES
Tập 6 Số 4 - Trang 379-406 - 1996
Darrell Duffie, Rui Kan

This paper presents a consistent and arbitrage‐free multifactor model of the term structure of interest rates in which yields at selected fixed maturities follow a parametric muitivariate Markov diffusion process with “stochastic volatility.” the yield of any zero‐coupon bond is taken to be a maturity‐dependent affine combination of the selected “basis” set of yields. We provide necessary and sufficient conditions on the stochastic model for this affine representation. We include numerical techniques for solving the model, as well as numerical techniques for calculating the prices of term‐structure derivative prices. the case of jump diffusions is also considered.

MAXIMUM LIKELIHOOD ESTIMATION USING PRICE DATA OF THE DERIVATIVE CONTRACT
Tập 4 Số 2 - Trang 155-167 - 1994
Jin‐Chuan Duan

This article develops a general methodology that uses the observed prices of a derivative contract to compute maximum likelihood parameter estimates for an unobserved asset value process. the use of this estimation methodology is demonstrated in two applications: Vasicek's term structure model and deposit insurance pricing. This methodology can also be useful in the empirical analysis of complex financial contracts involving embedded options.

BEHAVIORAL PORTFOLIO SELECTION IN CONTINUOUS TIME
Tập 18 Số 3 - Trang 385-426 - 2008
Hanqing Jin, Xun Yu Zhou

This 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 do not coordinate well with each other. Certain classes of an ill‐posed model are identified. A systematic approach, which is fundamentally different from the ones employed for the utility model, is developed to solve a well‐posed model, assuming a complete market and general Itô processes for asset prices. The optimal terminal wealth positions, derived in fairly explicit forms, possess surprisingly simple structure reminiscent of a gambling policy betting on a good state of the world while accepting a fixed, known loss in case of a bad one. An example with a two‐piece CRRA utility is presented to illustrate the general results obtained, and is solved completely for all admissible parameters. The effect of the behavioral criterion on the risky allocations is finally discussed.

Complete Models with Stochastic Volatility
Tập 8 Số 1 - Trang 27-48 - 1998
David Hobson, L. C. G. Rogers

The 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 nonconstant volatility, it is not necessary to introduce additional sources of randomness. Thus the market is complete and there are unique, preference‐independent options prices.

We find a partial differential equation for the price of a European call option. Smiles and skews are found in the resulting plots of implied volatility.

A DIFFUSION MODEL FOR ELECTRICITY PRICES
Tập 12 Số 4 - Trang 287-298 - 2002
Takashi Kumagai

Starting 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.

TRACTABLE ROBUST EXPECTED UTILITY AND RISK MODELS FOR PORTFOLIO OPTIMIZATION
Tập 20 Số 4 - Trang 695-731
Karthik Natarajan, Melvyn Sim, Joline Uichanco
OPTIMAL INSURANCE DESIGN UNDER RANK‐DEPENDENT EXPECTED UTILITY
Tập 25 Số 1 - Trang 154-186 - 2015
Carole Bernard, Xuedong He, Jia-an Yan, Xun Yu Zhou

We 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 solve the problem explicitly. We show that the optimal contract not only insures large losses above a deductible but also insures small losses fully. This is consistent, for instance, with the demand for warranties. Finally, we compare our results, analytically and numerically, both to those in the expected utility framework and to cases in which the distortion function is convex or concave.

Explicit Representation of the Minimal Variance Portfolio in Markets Driven by Lévy Processes
Tập 13 Số 1 - Trang 55-72 - 2003
Fred Espen Benth, Giulia Di Nunno, Arne Løkka, Frank Proske

In 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 one based on the chaos expansion in terms of iterated integrals with respect to the Wiener process and the Poisson random measure components. We study the relation between these two expansions, the corresponding two derivatives, and the corresponding versions of the Clark‐Haussmann‐Ocone theorem.