Motivated by Cont and Larrard (2013)'s seminal Limit Order Book (LOB) model, we propose two continuous-time models for the level I of a LOB in which the arrivals of limit orders, market orders, and cancellations are assumed to be mutually independent, memoryless, and stationary, but, unlike the...

We introduce a general framework of the Mixed-correlated ARFIMA (MC-ARFIMA) processes which allows for various specifications of univariate and bivariate long-term memory. Apart from a standard case when $H_{xy}={1}{2}(H_x+H_y)$, MC-ARFIMA also allows for processes with $H_{xy}{1}{2}(H_x+H_y)$...

We obtain stability estimates and derive analytic expansions for local solutions of multi-dimensional quadratic BSDEs. We apply these results to a financial model where the prices of risky assets are quoted by a representative dealer in such a way that it is optimal to meet an exogenous demand....

This paper studies the connection between Dynkin games and optimal switching in continuous time and on a finite horizon. An auxiliary two-mode optimal switching problem is formulated which enables the derivation of the game's value under very mild assumptions. Under slightly stronger...

The main goal of this paper is presentation a modern axiomatic approach to financial arithmetic. At the first, the axiomatic financial arithmetic theory was proposed by Peccati who has introduced the axiomatic definition of the future value. This theory has been extensively developed in past...

For a given Markov process $X$ and survival function $\overline H$ on $\mathbb R^+$, the inverse first-passage time problem (IFPT) is to find a barrier function $b:\mathbb R^+\to[-\infty,+\infty]$ such that the survival function of the first-passage time $\tau_b=\inf\{t\ge0: X(t) b(t)\}$ is...

We investigate the statistics of the gap, G_n, between the two rightmost positions of a Markovian one-dimensional random walker (RW) after n time steps and of the duration, L_n, which separates the occurrence of these two extremal positions. The distribution of the jumps \eta_i's of the RW,...

Investors who optimize their portfolios under any of the coherent risk measures are naturally led to regularized portfolio optimization when they take into account the impact their trades make on the market. We show here that the impact function determines which regularizer is used. We also show...

We characterize the set of market models when there are a finite number of traded Vanilla and Barrier options with maturity $T$ written on the asset $S$. From a probabilistic perspective, our result describes the set of joint distributions for $(S_T, \sup_{u \leq T} S_u)$ when a finite number of...

The one-dimensional SDE with non Lipschitz diffusion coefficient $dX_{t} = b(X_{t})dt + \sigma X_{t}^{\gamma} dB_{t}, \ X_{0}=x, \ \gamma1$ is widely studied in mathematical finance. Several works have proposed asymptotic analysis of densities and implied volatilities in models involving...