Invariance times are stopping times $ \tau $ such that local martingales with respect to some reduced filtration and an equivalently changed probability measure, stopped before $ \tau $, are local martingales with respect to the original model filtration and probability measure. They arise naturally for modeling the default time of a dealer bank, in the mathematical finance context of counterparty credit risk. Assuming an invariance time endowed with an intensity and a positive Azéma supermartingale, this work establishes a dictionary relating the semimartingale calculi in the original and reduced stochastic bases, regarding conditional expectations, martingales, stochastic integrals, random measure stochastic integrals, martingale representation properties, semimartingale characteristics, Markov properties, transition semigroups and infinitesimal generators, and solutions of backward stochastic differential equations.

In this study, we investigate the well-posedness of exponential growth backward stochastic differential equations (BSDEs) driven by a marked point process (MPP) under unbounded terminal conditions. Our analysis utilizes a fixed-point argument, the $\theta$-method, and an approximation procedure. Additionally, we establish the solvability of mean-reflected exponential growth BSDEs driven by the MPP using the $\theta$-method.

In this paper, we present a new precipitation model based on a multi-factor Ornstein-Uhlenbeck approach of pure-jump type. In this setup, we derive a representation for the related precipitation swap price process and infer its risk-neutral time dynamics. We further deduce a pricing formula for European options written on the precipitation swap and obtain the minimal variance hedging portfolio in the underlying weather market. In the second part of the paper, we provide a precipitation swap price representation under future information modeled by an initially enlarged filtration. We finally derive a formula for the associated information premium and investigate minimal variance hedging of precipitation derivatives under future information.

This paper studies the optimal pairs trading strategy of the mean−variance (MV) objective function under a continuous-time cointegration model with a common stochastic factor. Although this common stochastic factor is not directly tradable, it significantly impacts asset prices. We first provide a semiclosed-form solution under a general model. We then specify the common factor model to be a mean-reverting process with time-varying parameters and provide closed-form optimal strategies for pairs trading with fixed and flexible ratios, respectively. Empirical analysis based on historical data from Chinese securities markets shows the effectiveness of both optimal strategies. The optimal flexible-ratio strategy outperforms the optimal fixed-ratio strategy in terms of both profit and risk.

In this paper, we study one-dimensional backward stochastic differential equations featuring two reflecting barriers. When the terminal time is not necessarily bounded or finite and the generator $f(t, y, z)$ exhibits quadratic growth in $z$, we prove existence and uniqueness of solutions. In the Markovian case, we establish the link with an obstacle problem for quadratic elliptic partial differential equation with Dirichlet boundary conditions.

Let ${B}^{H}$ be a fractional Brownian motion with Hurst index $\frac{1}{2}\le H＜1$. In this paper, we consider the self-repelling diffusion ${X}_{t}^{H}={B}_{t}^{H}+\underset{0}{\overset{t}{{\displaystyle \int }}}\underset{0}{\overset{s}{{\displaystyle \int }}}g(u)\text{d}{X}_{u}^{H}\text{d}s+\nu t$,where $\nu \in ℝ$, and $g$ is a nonnegative Borel function. The process is an analogue of linear self-interacting diffusion (M. Cranston and Y. Le Jan Math. Ann. 303 (1995), 87-93.). Based on the asymptotic behavior of the weight function $g$ at infinity, we establish the large time behavior of the recursive convergence of the solution ${X}^{H}$. For example, when $g\in {C}^{\infty }({ℝ}_{+})$ and $0<g(t) \rightarrow+\infty(t \rightarrow+\infty)$, we demonstrate that there is a sequence $\left\{{\lambda }_{n}\right\}$ of positive real numbers such that $J_{t}^{H}(0 ; g):=g(t) e^{-G(t)} X_{t}^{H} \rightarrow \nu+\xi_{\infty}^{H}$ and $J_{t}^{H}(n ; g):=G(t)\left(J_{t}^{H}(n-1 ; g)-\lambda_{n-1}\left(\xi_{\infty}^{H}+\nu\right)\right) \longrightarrow \lambda_{n}\left(\xi_{\infty}^{H}+\nu\right) \quad(t \rightarrow+\infty)$ in ${L}^{2}$ and almost surely for every $n\in \{1,2,\dots \}$, where $G(t)=\underset{0}{\overset{t}{{\displaystyle \int }}}g(s)\text{d}s$ and $\xi_{\infty}^{H}:=\int_{0}^{\infty} g(r) e^{-G(r)} \mathrm{d} B_{r}^{H}$.