数理金融

We consider the valuation problem of an (insurance) company under partial information. Therefore we use the concept of maximizing discounted future dividend payments. The firm value process is described by a diffusion model with constant…

We determine the optimal investment strategy in a Black-Scholes financial market to minimize the so-called {\it probability of drawdown}, namely, the probability that the value of an investment portfolio reaches some fixed proportion of its…

Fractionally integrated generalized autoregressive conditional heteroskedasticity (FIGARCH) arises in modeling of financial time series. FIGARCH is essentially governed by a system of nonlinear stochastic difference equations ${u_t}$ =…

Consider the problem of pricing options on forwards in energy markets, when spot prices follow a geometric multi-factor model in which several rates of mean reversion appear. In this paper we investigate the role played by slow mean…

We consider a financial market where stocks are available for dynamic trading, and European and American options are available for static trading (semi-static trading strategies). We assume that the American options are infinitely…

In this note, we study the utility maximization problem on the terminal wealth under proportional transaction costs and bounded random endowment. In particular, we restrict ourselves to the num\'eraire-based model and work with utility…

In this paper we analyze an extension of the Jeanblanc and Valchev (2005) model by considering a short-term uncertainty model with two noises. It is a combination of the ideas of Duffie and Lando (2001) and Jeanblanc and Valchev (2005):…

We propose two methods to obtain exact solutions for the Almgren-Chriss model about optimal execution of portfolio transactions. In the first method we rewrite the Almgren-Chriss equation and find two exact solutions. In the second method,…

We obtain explicit representations of locally risk-minimizing strategies of call and put options for the Barndorff-Nielsen and Shephard models, which are Ornstein--Uhlenbeck-type stochastic volatility models. Using Malliavin calculus for…

In this paper, we study a continuous time structural asset value model for two correlated firms using a two-dimensional Brownian motion. We consider the situation of incomplete information, where the information set available to the market…

We show that the martingale component in the long-term factorization of the stochastic discount factor due to Alvarez and Jermann (2005) and Hansen and Scheinkman (2009) is highly volatile, produces a downward-sloping term structure of bond…

We discuss a simple extension of the Ho and Lee model with generic time-dependent drift in which: 1) we compute bond prices analytically; 2) the yield curve is sensible and the asymptotic yield is positive; and 3) our analytical solution…

This paper studies the problem of trading futures with transaction costs when the underlying spot price is mean-reverting. Specifically, we model the spot dynamics by the Ornstein-Uhlenbeck (OU), Cox-Ingersoll-Ross (CIR), or exponential…

This paper addresses the identification of insurance models with multidimensional screening where insurees have private information about their risk and risk aversion. The model includes a random damage and the possibility of several…

This paper introduces a dual problem to study a continuous-time consumption and investment problem with incomplete markets and stochastic differential utility. For Epstein-Zin utility, duality between the primal and dual problems is…

The probability minimizing problem of large losses of portfolio in discrete and continuous time models is studied. This gives a generalization of quantile hedging presented in [3].

In the paper a problem of risk measures on a discrete-time market model with transaction costs is studied. Strategy effectiveness and shortfall risk is introduced. This paper is a generalization of quantile hedging presented in [4].

We consider an optimal trading problem over a finite period of time during which an investor has access to both a standard exchange and a dark pool. We take the exchange to be an order-driven market and propose a continuous-time setup for…

R. Cont and A. de Larrard (SIAM J. Finan. Math, 2013) introduced a tractable stochastic model for the dynamics of a limit order book, computing various quantities of interest such as the probability of a price increase or the diffusion…

The main objective is to present a some variant of the Black - Litterman model. We consider the canonical case when priori return is determined by means such excess return from the CAPM market portfolio which is derived using reverse…