Related papers: Retarded action principle and self-financing portf…
The variance measures the portfolio risks the investors are taking. The investor, who holds his portfolio and doesn't trade his shares, at the current time can use the time series of the market trades that were made during the averaging…
This paper is concerned with a time-inconsistent recursive stochastic control problems where the forward state process is constrained through an additional recursive utility system. By adapting the Ekeland variational principle, necessary…
Suppose an investor aims at Delta hedging a European contingent claim $h(S(T))$ in a jump-diffusion model, but incorrectly specifies the stock price's volatility and jump sensitivity, so that any hedging strategy is calculated under a…
This paper studies the dynamic programming principle using the measurable selection method for stochastic control of continuous processes. The novelty of this work is to incorporate intermediate expectation constraints on the canonical…
In a recent paper (Abe S 2013 Phys. Rev. E 88 022142), a variational principle has been formulated for spatiotemporally-fractional Fokker-Planck equations and applied to derivations of their approximate analytic solutions based on the…
We study singular stochastic control of a two dimensional stochastic differential equation, where the first component is linear with random and unbounded coefficients. We derive existence of an optimal relaxed control and necessary…
In this paper we develop a concrete and fully implementable approach to the optimization of functionally generated portfolios in stochastic portfolio theory. The main idea is to optimize over a family of rank-based portfolios parameterized…
We consider the hedging error of a derivative due to discrete trading in the presence of a drift in the dynamics of the underlying asset. We suppose that the trader wishes to find rebalancing times for the hedging portfolio which enable him…
A treatment policy defines when and what treatments are applied to affect some outcome of interest. Data-driven decision-making requires the ability to predict what happens if a policy is changed. Existing methods that predict how the…
We consider the valuation of contingent claims with delayed dynamics in a Black&Scholes complete market model. We find a pricing formula that can be decomposed into terms reflecting the market values of the past and the present, showing how…
Stochastic volatility models describe stock returns $r_t$ as driven by an unobserved process capturing the random dynamics of volatility $v_t$. The present paper quantifies how much information about volatility $v_t$ and future stock…
This paper presents a synthesis of the theories of portfolio generating functions and option pricing. The theory of portfolio generation is extended to measure the value of portfolios generated by positive C^{2,1} functions of asset prices…
Portfolio's optimal drivers for diversification are common causes of the constituents' correlations. A closed-form formula for the conditional probability of the portfolio given its optimal common drivers is presented, with each pair…
Scalar dynamic risk measures for univariate positions in continuous time are commonly represented as backward stochastic differential equations. In the multivariate setting, dynamic risk measures have been defined and studied as families of…
We introduce a new model of financial market with stochastic volatility driven by an arbitrary H\"older continuous Gaussian Volterra process. The distinguishing feature of the model is the form of the volatility equation which ensures the…
We extend and test empirically the multifractal model of asset returns based on a multiplicative cascade of volatilities from large to small time scales. The multifractal description of asset fluctuations is generalized into a multivariate…
A kinetic equation is derived for the phase density of a system of point particles, generating a system of integro-differential equations for distribution functions that have a deterministic meaning. The derivation took into account the…
We study an optimal investment/consumption problem in a model capturing market and credit risk dependencies. Stochastic factors drive both the default intensity and the volatility of the stocks in the portfolio. We use the martingale…
The equivalence between multiportfolio time consistency of a dynamic multivariate risk measure and a supermartingale property is proven. Furthermore, the dual variables under which this set-valued supermartingale is a martingale are…
This paper investigates the so-called leakage effect of trading strategies generated functionally from rank-dependent portfolio generating functions. This effect measures the loss in wealth of trading strategies due to renewing the…