Related papers: Mimicking an It\^{o} process by a solution of a st…
We study the estimation of time-homogeneous drift functions in multivariate stochastic differential equations with known diffusion coefficient, from multiple trajectories observed at high frequency over a fixed time horizon. We formulate…
We consider a controlled diffusion process $(X_t)_{t\ge 0}$ where the controller is allowed to choose the drift $\mu_t$ and the volatility $\sigma_t$ from a set $\K(x) \subset \R\times (0,\infty)$ when $X_t=x$. By choosing the largest…
We study large deviation properties of systems of weakly interacting particles modeled by It\^{o} stochastic differential equations (SDEs). It is known under certain conditions that the corresponding sequence of empirical measures…
This paper studies equity basket options -- i.e., multi-dimensional derivatives whose payoffs depend on the value of a weighted sum of the underlying stocks -- and develops a new and innovative approach to ensure consistency between options…
The asymptotic behavior, as $T\to\infty$, of some functionals of the form $I_T(t)=F_T(\xi_T(t))+\int_0^tg_T(\xi_T(s))\,dW_T(s)$, $t\ge0$ is studied. Here $\xi_T(t)$ is the solution to the time-inhomogeneous It\^{o} stochastic differential…
Complex behaviour in many systems arises from the stochastic interactions of spatially distributed particles or agents. Stochastic reaction-diffusion processes are widely used to model such behaviour in disciplines ranging from biology to…
In this paper we prove a discretized version of Krylov's estimate for discretized It\^o's processes. As applications, we study the weak and strong convergences for Euler's approximation of mean-field SDEs with measurable discontinuous and…
This thesis develops a new framework for modelling price processes in finance, such as an equity price or foreign exchange rate. This can be related to the conventional Ito calculus-based framework through the time integral of a price's…
In this paper we provide a comprehensive analysis of a structural model for the dynamics of prices of assets traded in a market originally proposed in [1]. The model takes the form of an interacting generalization of the geometric Brownian…
We propose a new simple and explicit numerical scheme for time-homogeneous stochastic differential equations. The scheme is based on sampling increments at each time step from a skew-symmetric probability distribution, with the level of…
This paper considers approximate smoothing for discretely observed non-linear stochastic differential equations. The problem is tackled by developing methods for linearising stochastic differential equations with respect to an arbitrary…
Many physical processes depend on the time it takes a diffusing particle to find a target. Though this classical quantity is now well-understood in various scenarios, little is known if the diffusivity depends on the location of the…
This paper develops systematically the stochastic calculus via regularization in the case of jump processes. In particular one continues the analysis of real-valued c\`adl\`ag weak Dirichlet processes with respect to a given filtration.…
We provide results of a deterministic approximation for non-Markovian stochastic processes modeling finite populations of individuals who recurrently play symmetric finite games and imitate each other according to payoffs. We show that a…
We consider the use of adaptive timestepping to allow a strong explicit Euler-Maruyama discretisation to reproduce dynamical properties of a class of nonlinear stochastic differential equations with a unique equilibrium solution and…
The existence of a weak solution to a McKean-Vlasov type stochastic differential system corresponding to the Enskog equation of the kinetic theory of gases is established under natural conditions. The distribution of any solution to the…
Assuming frictionless trading, classical stochastic portfolio theory (SPT) provides relative arbitrage strategies. However, the costs associated with real-world execution are state-dependent, volatile, and under increasing stress during…
We present a Bayesian non-parametric way of inferring stochastic differential equations for both regression tasks and continuous-time dynamical modelling. The work has high emphasis on the stochastic part of the differential equation, also…
We first prove a mimicking theorem (also known as a Markovian projection theorem) for the marginal distributions of an Ito process conditioned to not have exited a given domain. We then apply this new result to the proof of a conjecture of…
The existence and uniqueness of probabilistic solutions of variational inequalities for the general American options are proved under the hypothesis of hypoellipticity of the infinitesimal generator of the underlying diffusion process which…