In this paper we present a slight modification of the Fourier estimation method of the spot volatility (matrix) process of a continuous It\^o semimartingale where the estimators are always non-negative definite. Since the estimators are factorized, computational cost will be saved a lot.

Modelling of contagion in interbank networks is discussed. A model taking into account bow-tie structure and dissasortativity of interbank networks is developed. The model is shown to provide a good quantitative description of the Russian interbank market. Detailed arguments favoring the...

We study utility indifference prices and optimal purchasing quantities for a non-traded contingent claim in an incomplete semi-martingale market with vanishing hedging errors, making connections with the theory of large deviations. We concentrate on sequences of semi-complete markets where for...

A fundamental problem in risk management is the robust aggregation of different sources of risk in a situation where little or no data are available to infer information about their dependencies. A popular approach to solving this problem is to formulate an optimization problem under which one...

In this work, we consider the optimal portfolio selection problem under hard constraints on trading volume amounts when the dynamics of the risky asset returns are governed by a discrete-time approximation of the Markov-modulated geometric Brownian motion. The states of Markov chain are...

In this paper, we prove the global risk optimality of the hedging strategy of contingent claim, which is explicitly (or called semi-explicitly) constructed for an incomplete financial market with external risk factors of non-Gaussian Ornstein-Uhlenbeck (NGOU) processes. Analytical and numerical...

We develop a simple and general method for solving non-linear Hamilton-Jacobi-Bellman partial differential equations HJB PDEs. We apply our method to the portfolio model.

A motivating question in this paper is whether a sensible investment strategy may systematically contain long positions in out-of-the-money European calls with short expiry. Here we consider a very simple trading strategy for calls. The main points of this note are the following. First, the...

In this paper we discuss the possibility of using multilevel Monte Carlo (MLMC) methods for weak approximation schemes. It turns out that by means of a simple coupling between consecutive time discretisation levels, one can achieve the same complexity gain as under the presence of a strong...

We investigate the role of networks of alliances in preventing (multilateral) interstate wars. We first show that, in the absence of international trade, no network of alliances is peaceful and stable. We then show that international trade induces peaceful and stable networks: trade increases...