Finance and Stochastics
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Modelling of stock price changes: A real analysis approach
Finance and Stochastics - Tập 4 - Trang 343-369 - 2000
Abstract. In this paper a real analysis approach to stock price modelling is considered. A stock price and its return are defined in a duality to each other provided there exist suitable limits along a sequence of nested partitions of a time interval, mimicking sum and product integrals. It extends the class of stochastic processes susceptible to theoretical analysis. Also, it is shown that exte......
Nonparametric estimation for i.i.d. paths of a martingale-driven model with application to non-autonomous financial models
Finance and Stochastics - - 2023
Jump-robust estimation of volatility with simultaneous presence of microstructure noise and multiple observations
Finance and Stochastics - Tập 21 - Trang 427-469 - 2017
In this paper, we develop the multipower estimators for the integrated volatility in (Barndorff-Nielsen and Shephard in J. Financ. Econom. 2:1–37, 2004); these estimators allow the presence of jumps in the underlying driving process and the simultaneous presence of microstructure noise and multiple records of observations. By multiple records we mean more than one observation recorded on a single ......
Optimal Early Retirement Near the Expiration of a Pension Plan
Finance and Stochastics - Tập 10 - Trang 204-221 - 2006
In a recent paper, Friedman and Shen (Finance Stoch 6: 273–302, 2002) have considered a pension plan with the option of early retirement. They showed that the financial value V of the retirement benefits is the solution of a variational inequality and have studied the associated free boundary. A description of the free boundary near maturity is given, thanks to integral equation methods. However, ......
The joint distribution of Parisian and hitting times of Brownian motion with application to Parisian option pricing
Finance and Stochastics - Tập 20 - Trang 773-804 - 2016
We study the joint law of Parisian time and hitting time of a drifted Brownian motion by using a three-state semi-Markov model, obtained through perturbation. We obtain a martingale to which we can apply the optional sampling theorem and derive the double Laplace transform. This general result is applied to address problems in option pricing. We introduce a new option related to Parisian options, ......
Optimal dividend payouts for diffusions with solvency constraints
Finance and Stochastics - Tập 7 - Trang 457-473 - 2003
We consider a company where surplus follows a diffusion process and whose objective is to maximize expected discounted dividend payouts to the shareholders. It is well known that under some reasonable assumptions, optimality is achieved by using a barrier strategy, i.e. there is a level b* so that whenever suplus goes above b*, the excess is paid out as dividends. However, the optimal level b* ma......
Financial equilibrium with asymmetric information and random horizon
Finance and Stochastics - Tập 22 Số 1 - Trang 97-126 - 2018
Optimal dividend distribution under Markov regime switching
Finance and Stochastics - Tập 16 - Trang 449-476 - 2012
We investigate the problem of optimal dividend distribution for a company in the presence of regime shifts. We consider a company whose cumulative net revenues evolve as a Brownian motion with positive drift that is modulated by a finite state Markov chain, and model the discount rate as a deterministic function of the current state of the chain. In this setting, the objective of the company is to......
On a general class of one-factor models for the term structure of interest rates
Finance and Stochastics - Tập 1 - Trang 3-24 - 1996
We propose a general one-factor model for the term structure of interest rates which based upon a model for the short rate. The dynamics of the short rate is described by an appropriate function of a time-changed Wiener process. The model allows for perfect fitting of given term structure of interest rates and volatilities, as well as for mean reversion. Moreover, every type of distribution of the......
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