Finance and Stochastics
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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 ......
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, ......
Pathwise superhedging on prediction sets
Finance and Stochastics - Tập 24 Số 1 - Trang 215-248 - 2020
In this paper, we provide a pricing–hedging duality for the model-independent superhedging price with respect to a prediction set $\Xi \subseteq C[0,T]$, where the superhedging property needs to hold pathwise, but only for paths lying in $\Xi $. For any Borel-measurable claim $\xi $ bounded from below, the superhedging price coincides with the supremum over all pricing functionals $\mathbb{E}_{\ma......
Infinite-dimensional polynomial processes
Finance and Stochastics - Tập 25 - Trang 383-426 - 2021
We introduce polynomial processes taking values in an arbitrary Banach space
${B}$
via their infinitesimal generator
$L$
and the associated martingale problem. We obtain two representations of the......
Robust representation of convex risk measures by probability measures
Finance and Stochastics - - 2005
Asset pricing with dynamically inconsistent agents
Finance and Stochastics - Tập 27 - Trang 1017-1046 - 2023
This paper investigates an endowment economy featuring dynamically inconsistent preferences. Taking a game-theoretic approach, the paper provides an explicit characterisation of the market equilibrium, including the equilibrium short rate, the equilibrium market price of risk and the equilibrium stochastic discount factor. The general results are applied to models featuring non-exponential discoun......
Faking Brownian motion with continuous Markov martingales
Finance and Stochastics - Tập 28 - Trang 259-284 - 2023
Hamza and Klebaner (2007) [10] posed the problem of constructing martingales with one-dimensional Brownian marginals that differ from Brownian motion, so-called fake Brownian motions. Besides its theoretical appeal, this problem represents the quintessential version of the ubiquitous fitting problem in mathematical finance where the task is to construct martingales that satisfy marginal constraint......
A model of optimal portfolio selection under liquidity risk and price impact
Finance and Stochastics - Tập 11 - Trang 51-90 - 2006
We study a financial model with one risk-free and one risky asset subject to liquidity risk and price impact. In this market, an investor may transfer funds between the two assets at any discrete time. Each purchase or sale policy decision affects the rice of the risky asset and incurs some fixed transaction cost. The objective is to maximize the expected utility from terminal liquidation value ov......
The dynamics of strategic information flows in stock markets
Finance and Stochastics - Tập 12 - Trang 43-82 - 2007
We model a stock market with multiple stocks in a dynamic setting. Multiple informed traders receive new and heterogeneous information about the stocks in each period and use this information strategically. We characterize the decay rate of the information as it is incorporated into prices. The presence of multiple assets speeds information release by providing more channels for market makers to ......
Tangent Lévy market models
Finance and Stochastics - Tập 16 - Trang 63-104 - 2011
In this paper, we introduce a new class of models for the time evolution of the prices of call options of all strikes and maturities. We capture the information contained in the option prices in the density of some time-inhomogeneous Lévy measure (an alternative to the implied volatility surface), and we set this static code-book in motion by means of stochastic dynamics of Itô’s type in a functio......
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