Related papers: Long Term Risk: A Martingale Approach
Explicit robust hedging strategies for convex or concave payoffs under a continuous semimartingale model with uncertainty and small transaction costs are constructed. In an asymptotic sense, the upper and lower bounds of the cumulative…
The paper is concerned with stochastic equations for the short rate process $R$ $$ dR(t)=F(R(t))dt+G(R(t-))dZ(t), $$ in the affine model of the bond prices. The equation is driven by a L\'evy martingale $Z$. It is shown that the discounted…
The paper [12] examines a concept of equilibrium policies instead of optimal controls in stochastic optimization to analyze a mean-variance portfolio selection problem. We follow the same approach in order to investigate the Merton…
We show that prediction performance for global-local shrinkage regression can overcome two major difficulties of global shrinkage regression: (i) the amount of relative shrinkage is monotone in the singular values of the design matrix and…
We consider a general piecewise deterministic Markov process (PDMP) $X=\{X_t\}_{t\geqslant 0}$ with measure-valued generator $\mathcal{A}$, for which the conditional distribution function of the inter-occurrence time is not necessarily…
Systemic risk measures are crucial for the stability of financial markets, yet classical formulations fail to capture the complexity of market volatility. We propose a new framework for systemic risk measurement on the variable-exponent…
Systemic risk is the risk that a company- or industry-level risk could trigger a huge collapse of another or even the whole institution. Various systemic risk measures have been proposed in the literature to quantify the domino and…
This paper presents a convenient framework for modeling default process and pricing derivative securities involving credit risk. The framework provides an integrated view of credit valuation adjustment by linking distance-to-default,…
In this paper, we obtain stability results for martingale representations in a very general framework. More specifically, we consider a sequence of martingales each adapted to its own filtration, and a sequence of random variables…
The paper tests the validity of the critique of the fiscal theory of the price level. A stochastic general equilibrium model with continuous time is constructed. An active fiscal policy and a passive monetary policy have been set. Monetary…
Estimating time-varying correlation matrices is challenging because existing methods may adapt slowly to structural changes, impose insufficient regularization, or produce diffuse posterior uncertainty. In moderate dimensions, an additional…
Computing the marginal likelihood or evidence is one of the core challenges in Bayesian analysis. While there are many established methods for estimating this quantity, they predominantly rely on using a large number of posterior samples…
We introduce an approximation strategy for the discounted moments of a stochastic process that can, for a large class of problems, approximate the true moments. These moments appear in pricing formulas of financial products such as bonds…
The duality between the robust (or equivalently, model independent) hedging of path dependent European options and a martingale optimal transport problem is proved. The financial market is modeled through a risky asset whose price is only…
The purpose of this article is to describe all possible beliefs of market participants on objective measures under Markovian environments when a risk-neutral measure is given. To achieve this, we employ the Martin integral representation of…
Motivated by practical applications, we explore the constrained multi-period mean-variance portfolio selection problem within a market characterized by a dynamic factor model. This model captures predictability in asset returns driven by…
This paper contributes to the study of relative martingales. Specifically, for a closed random set $H$, they are processes null on $H$ which decompose as $M=m+v$, where $m$ is a c\`adl\`ag uniformly integrable martingale and, $v$ is a…
In this paper we study a continuous time, optimal stochastic investment problem under limited resources in a market with N firms. The investment processes are subject to a time-dependent stochastic constraint. Rather than using a dynamic…
We study a variant of the martingale optimal transport problem in a multi-period setting to derive robust price bounds of a financial derivative. On top of marginal and martingale constraints, we introduce a time-homogeneity assumption,…
In this paper we introduce a model, the stochastic fractional delay differential equation (SFDDE), which is based on the linear stochastic delay differential equation and produces stationary processes with hyperbolically decaying…