数理金融
This paper studies the equity holders' mean-variance optimal portfolio choice problem for (non-)protected participating life insurance contracts. We derive explicit formulas for the optimal terminal wealth and the optimal strategy in the…
An agent-based modelling methodology for the joint price evolution of two stocks is put forward. The method models future multidimensional price trajectories reflecting how a class of agents rebalance their portfolios in an operational way…
Modern financial networks involve complex obligations that transcend simple monetary debts: multiple currencies, prioritized claims, supply chain dependencies, and more. We present a mathematical framework that unifies and extends these…
In this work, we introduce a novel pricing methodology in general, possibly non-Markovian local stochastic volatility (LSV) models. We observe that by conditioning the LSV dynamics on the Brownian motion that drives the volatility, one…
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…
This article consolidates and extends past work on derivative pricing adjustments, including XVA, by providing an encapsulating representation of the adjustment between any two derivative pricing functions, within an Ito SDE/parabolic PDE…
We propose a new financial model, the stochastic volatility model with sticky drawdown and drawup processes (SVSDU model), which enables us to capture the features of winning and losing streaks that are common across financial markets but…
This study explores the application of Hawkes processes to model high-frequency data in the context of limit order books. Two distinct Hawkes-based models are proposed and analyzed: one utilizing exponential kernels and the other employing…
Suppose $\mu$ and $\nu$ are probability measures on $\mathbb R$ satisfying $\mu \leq_{cx} \nu$. Let $a$ and $b$ be convex functions on $\mathbb R$ with $a \geq b \geq 0$. We are interested in finding \[ \sup_{\mathcal M} \sup_{\tau}…
This paper builds on "Collective Arbitrage and the Value of Cooperation" by Biagini et al. (2025, forthcoming in "Finance and Stochastics"), which introduced in discrete time the notions of collective arbitrage and super-replication in a…
We establish deterministic necessary and sufficient conditions for the no-arbitrage notions "no increasing profit" (NIP), "no strong arbitrage" (NSA) and "no unbounded profit with bounded risk" (NUPBR) in one-dimensional general diffusion…
The existence of optimal contracts of the principal-agent problem is a long-standing problem. According to the general framework in Cvitani\'c et al. [2], this existence can be derived from the existence of a classical solution to a…
We introduce a model-free approach for analyzing the risk and return for a broad class of dynamic trading strategies, including pairs trading, mean-reversion trading and other statistical arbitrage strategies, in terms of excursions of a…
Using introduced concept of the exchange and inflation rates adequacy, the relevance of them to the determining factors is found. We established close positive relation between hryvnia / dollar exchange and inflation rates, fiscal deficit,…
This paper provides evidence that stock returns, after truncation, might be modeled by a special type of continuous mixtures or normals, so-called $q$-Gaussians. Negative binomial distributions might model the counts for extreme returns. A…
The standard approach for constructing a Mean-Variance portfolio involves estimating parameters for the model using collected samples. However, since the distribution of future data may not resemble that of the training set, the…
In this paper, we will show that under certain conditions, associated to any fixed distortion function $g$, the distortion risk measure of a sum of two counter-monotonic risks can be expressed as the sum of two related distortion risk…
We formulate and solve an optimal trading problem with alpha signals, where transactions induce a nonlinear transient price impact described by a general propagator model, including power-law decay. Using a variational approach, we…
In this paper, we introduce a robust market making framework based on Wasserstein distance, utilizing a stochastic policy approach enhanced by entropy regularization. We demonstrate that, under mild assumptions, the robust market making…
We provide a constructive way of defining new elicitable risk measures that are characterised by a multiplicative scoring function. We show that depending on the choice of the scoring function's components, the resulting risk measure…