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Sharp Inequalities for Linear Combinations of Orthogonal Martingales
For any two real-valued continuous-path martingales X = { X t } t ≥0 and Y = { Y t } t ≥0 , with X and Y being orthogonal and Y being differentially subordinate...
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Martingale Orlicz-Hardy spaces for continuous-time
We introduce several martingale Orlicz-Hardy spaces with continuous time. By use of the atomic decomposition, we establish some...
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Optimal investment based on relative performance and weighted utility
This paper studies the optimal portfolio allocation of a fund manager when he bases decisions on both the absolute level of terminal relative...
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Statistical causality, optional and predictable projections*
We consider the statistical concept of causality in continuous time within filtered probability spaces based on Granger’s definition of causality....
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A Variational Characterization of Langevin-Smoluchowski Diffusions
We show that Langevin–Smoluchowski measure on path space is invariant under time-reversal, followed by stochastic control of the drift with a novel...
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Martingale method for optimal investment and proportional reinsurance
Numerous researchers have applied the martingale approach for models driven by Lévy processes to study optimal investment problems. This paper...
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Wasserstein Distance Estimates for Stochastic Integrals by Forward-Backward Stochastic Calculus
We prove Wasserstein distance bounds between the probability distributions of stochastic integrals with jumps, based on the integrands appearing in...
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Interpolation Between Continuous Parameter Martingale Hardy–Lorentz and BMO Spaces
In this paper, we consider continuous parameter martingale Hardy–Lorentz spaces and describe their real interpolation spaces when we apply function...
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Minimal variance hedging in multicurve interest rate modeling
We consider minimal variance hedging in a pure-jump multicurve interest rate model. In the first part, we derive arithmetic multifactor martingale...
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An Actuarial Approach to Reload Option Valuation for a Non-tradable Risk Assets under Jump-diffusion Process and Stochastic Interest Rate
We use an actuarial approach to estimate the valuation of the reload option for a non-tradable risk asset under the jump-diffusion processes and...
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Variance-Optimal Martingale Measures for Diffusion Processes with Stochastic Coefficients
In this paper we present the solution of the optimal variance optimal martingale measure for stochastic volatility models, when the noises are...
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Granger causality and stop** times*
We consider causality relationships between σ -fields (filtrations) associated by stop** times, which can be applied to the stopped processes. These...
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A delayed stochastic volatility correction to the constant elasticity of variance model
The Black-Scholes model does not account non-Markovian property and volatility smile or skew although asset price might depend on the past movement...
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Weighted Inequalities for the Dyadic Square Function
We study Fefferman–Stein inequalities for the dyadic square function associated with an integrable, Hilbert-space-valued function on the interval [0,...
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Exponential martingale for compound Poisson process with latent variable and its applications
In this article, we construct an exponential martingale for the compound Poisson process with latent variable. With the help of this exponential...
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On the Existence of the Dual Right Markov Process and Applications
We show that given a Borel right process there exists a dual process which is also a right Markov process. However, it is necessary to enlarge the...
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Itô Calculus without Probability in Idealized Financial Markets*
We consider idealized financial markets in which price paths of the traded securities are càdlàg functions, imposing mild restrictions on the allowed...
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Sharp weak-type inequalities for Fourier multipliers and second-order Riesz transforms
We study sharp weak-type inequalities for a wide class of Fourier multipliers resulting from modulation of the jumps of Lévy processes. In...
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A sharp maximal inequality for continuous martingales and their differential subordinates
Assume that X , Y are continuous-path martingales taking values in ℝ ν , ν ⩾ 1, such that Y is differentially subordinate to X . The paper contains the...