New decomposition for submartingales aids American option hedging in incomplete markets.
problem Hedging American options in incomplete markets with jumps.
method Introduced nonlinear optional decomposition for Yg,ξ-submartingales. result Infinitesimal characterization of buyer's superhedging price.
Paper defines saddle points in asymmetric Dynkin games using martingale theory.
problem Tackles saddle point conditions in asymmetric Dynkin games with partial information.
method Uses martingale theory to identify super and submartingales related to equilibrium payoffs.
result Characterizes saddle point strategies in terms of equilibrium payoffs' dynamics and Doob-Meyer decompositions.
We first introduce the concept of Yg,ξ-submartingale systems, where the nonlinear operator Yg,ξ corresponds to the first component of the solution of a reflected BSDE with generator g and lower obstacle ξ. We first show that, in the case of a left-limited right-continuous obstacle, any…
Study on Kyle's model with stochastic liquidity impacts asset volatility.
problem Impact of stochastic volatility of noise trading on asset volatility.
method Construct equilibrium for continuous-time Kyle's model with stochastic liquidity.
result In equilibrium, Kyle's Lambda and its inverse are submartingales.
Model optimal growth strategy in a market with short-lived assets.
problem Investment market with short-lived assets and endogenous prices.
method Formulate stochastic equation for wealth processes and prove existence of optimal strategy.
result Existence of a submartingale strategy ensuring investor's wealth growth asymptotically.
A strategy ensures maximal wealth growth in competitive asset markets.
problem Maximizing wealth growth in competitive asset markets.
method Game-theoretic model and proof of existence of a submartingale strategy.
result Existence and uniqueness of a submartingale strategy that maximizes wealth growth.
New inequalities for matrix supermartingales converge under various conditions.
problem Convergence and maximal inequalities of supermartingales in positive semidefinite matrices.
method Developed new concentration inequalities for matrix supermartingales.
result New inequalities for matrix supermartingales under different tail conditions.
Study shows how margin loan interest rates converge to a choke price, limiting long-term advantage in the broker call money market.
problem Long-term dynamics of margin loan interest rates and their impact on retail clients' advantage in the broker call money market.
method Analyzes the broker call money market dynamics, assuming perfect inelastic supply and continuous reinvestment, to show convergence of relative size and margin loan interest rates.
result Margin loan interest rates converge to a choke price, limiting the long-term advantage of retail clients over the market.
A new XVA strategy rooted in balance sheet perspective improves equity process for bank shareholders.
problem Counterparty risk valuation adjustments (XVAs) in financial derivatives.
method Develops a cost-of-capital XVA strategy in a balance sheet perspective, solving explicitly in static setup and dynamically in trade context.
result Ensures a submartingale equity process corresponding to a target hurdle rate on capital at risk.
Unified technique for sequential estimation of convex divergences.
problem Estimating convex divergences between distributions.
method Martingale methods and maximal inequalities for reverse submartingales.
result Valid time-uniform confidence sequences for arbitrary stopping times.
Unified framework for anytime-valid PAC-Bayes bounds.
problem Deriving time-uniform PAC-Bayes bounds for stochastic processes.
method Combines four tools: nonnegative supermartingales, method of mixtures, Donsker-Varadhan formula, and Ville's inequality.
result Unified PAC-Bayes theorem for a wide class of discrete stochastic processes.
In this article, we follow the study of quadratic backward SDEs with jumps,that is to say for which the generator has quadratic growth in the variables (z; u), started in our accompanying paper [15]. Relying on the existence and uniqueness result of [15], we define the corresponding g-expectations and study some of the…
In this paper we extend the series of our studies on the properties of an interacting particle model for market microstructure. In our earlier work we defined a Markov process on the majority opinion of the agents, obtained the transition probabilities and analyzed the martingale properties of the ensuing wealth proces…
We study a robust Dynkin game over a set of mutually singular probabilities. We first prove that for the conservative player of the game, her lower and upper value processes coincide (i.e. She has a value process V in the game). Such a result helps people connect the robust Dynkin game with second-order doubly refle…
Model explains deleveraging risks in non-custodial stablecoins.
problem Deleveraging risks in non-custodial stablecoins during market crises.
method Developed a stochastic model incorporating speculators' profit optimization and collateral liquidation costs.
result Identified deflationary deleveraging spirals and higher price variance in unstable domains.
We extend Kyle's model to include stochastic liquidity and multiple assets.
problem Modeling informed trading with stochastic liquidity and multiple assets.
method Developed a variational formulation and derived a matrix-valued martingale depth process.
result A linear-Gaussian equilibrium with stochastic matrix-valued price impact.
Optimizes Iron Condor portfolios for better risk and profit management.
problem Transient value process of Iron Condor portfolios not well studied.
method Formulated as a stochastic optimal control problem, using bounded martingale assumption.
result Optimal stopping time aligns with expiration for submartingale value process.