1,720,983 research outputs found
Cauchy problem for nonautonomous Kolmogorov equations
No full textWe study the existence and uniqueness of the strict solutions of an initial value problem for a nonautonomous Kolmogorov equation in a space of unbounded functions
Non-differentiability of heat semigroups in infinite-dimensional Hilbert spaces
No full textWe consider the regularization effect of the heat semigroup in a separable Hilbert space. We prove that this semigroup is not differentiable
A statistical model for cellular proliferation
No full textThe evolution of a biological system, like a cellular one, is analyzed by constructing a Markov process on a suitable state space. This is performed by the introduction of an infinitesimal generator for the Markov semi-group associated to this process. A measure valued process is then defined in a natural way and it is proved that his first moment satisfies the Sharpe-Lotka system in a distributional sense. Hence the study of the moments of the process is tried. An involved integral equation for the moment generating functional is derived
Theory and calibration of HJM with shape factors
No full textWe reconstruct arbitrage free dynamics for the term structure of interest rates driven by infinitely many factors, each one representing a basic shape for the instantaneous forward rate curve in a given market. The consistency between a finite dimensional space of polynomials where the curve is day-to-day recovered and the proposed evolution equation is investigated. The main result is the developement of a historical-implicit hybrid calibration procedure for our infinite-dimensional shape factor model. In this context we also derive a pricing formula for caplets
the asymptotic behaviour of a proliferant-quiescent cell system
No full textThe authors study an age-structured model for the growth of cell populations. Their model accounts for the transition between different phases in the cell cycle and for transitions between proliferating and quiescent stages. In quiescence the maturation stops. Reproduction is assumed to occur via mitosis. The authors show the existence and the exponential stability of a stationary normalized age-distribution. This stationary normalized age-distribution corresponds to an exponentially growing solution of the cell-population model, where all components grow at the same rate. This rate, and the rate of convergence towards it, are derived from the model parameters. For the proof of stability the authors use Laplace transform methods, since the method of characteristics is not applicable
The geometry of Generating Functions for a class of Hamiltonians in the non compact case
No full textWe consider a class of Hamiltonians H:T⋆Rn⟶R and the related flows View the MathML source, proving the existence and uniqueness of generating functions quadratic at infinity for its graph View the MathML source. As a consequence, we obtain the same results for the Lagrangian submanifolds View the MathML source Hamiltonianly isotopic to the zero section L0≃Rn. This problem was also considered by Chaperon, Sikorav and Viterbo in the case of closed manifolds. The assumption on the class of Hamiltonians is an asymptotic behaviour of polynomial type on the phase space. In particular, we deal with a family of Hamiltonian systems arising from usual mechanical problems, for which we study the structure of the corresponding generating functions, showing their main analytical properties. The results presented in the paper are applied to prove the existence and uniqueness of minmax solutions for a class of Hamilton–Jacobi equations on T⋆Rn
Combined Custom Hedging: Optimal Design, Noninsurable Exposure, and Operational Risk Management
Full text linkWe develop a normative framework for the optimal design, value assessment,
and risk management integration of combined custom contingent claims. A risk-averse
firm faces a mix of financially insurable and noninsurable risk. The firm seeks optimal positioning in a pair of custom claims, one written on the insurable term and another written
on any listed index correlated to the noninsurable term. We prove that a unique optimum
always exists unless the index is redundant and show that the optimal payoff schedules
satisfy a design integral equation. We assess the firm’s incremental benefit in terms of both
an indifference value and an efficiency rating; this benefit increases with the correlation of
the index to the noninsurable term, and it decreases with the correlation of the index to the
insurable term. Our hedge proves to be empirically relevant for a highly risk-averse firm
facing a market shock (COVID-19 pandemic). In the context of a newsvendor model featuring random price and demand, we show that (i) integrating our optimal combined custom
hedge with the corresponding optimal procurement policy allows the firm to obtain a significant improvement in both risk and return, and (ii) this gain may be traded off for a substantial enhancement in operational flexibility
Integral representations for the Schroedinger propagator
No full textWe consider the Schro ̈dinger equation for a Hamiltonian operator with a potential function modeling one-particle scattering problems. By means of a
strongly converging regularization of the Schro ̈dinger propagator U(t), we introduce a new class
of integral representations for the relaxed kernel in terms of oscillatory integrals. They are
constructed with complex amplitudes and real phase functions that belong to the class of global
weakly quadratic generating functions of the Lagrangian submanifolds related to the group of classical canonical transformations. Moreover, as a particular generating function, we consider the action functional A[γ] evaluated on a suitable finite-dimensional space of curves γ ∈ Ŵ ⊂ H1([0,t],Rn). As a matter of fact we obtain a finite-dimensional path integral representation for the relaxed kernel
Shape Factor and Cross-Sectional Risk
Full text linkGalluccio and Roncoroni (2006) empirically demonstrate that cross-sectional data provide relevant information when assessing dynamic risk in fixed income markets. We put forward a theoretical framework supporting that finding based on the notion of "shape factors". We devise an econometric procedure to identify shape factors, propose a dynamic model for the yield curve, develop a corresponding arbitrage pricing theory, derive interest rate pricing formulae, and study the analytical properties exhibited by a finite factor restriction of rate dynamics that is cross-sectionally consistent with a family of exponentially weighed polynomials. We also conduct an empirical analysis of cross-sectional risk affecting US swap, Euro bond, and oil markets. Results support the conclusion whereby shape factors outperform the classical yield (resp., price) factors (i.e., level, slope, and convexity) in explaining the underlying fixed income (resp., commodity) market risk. The methodology can in principle be used for understanding the intertemporal dynamics of any cross-sectional data
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