Lie systems method simplifies Riccati hierarchy study.
problem Simplifying study of Riccati hierarchy equations.
method Lie systems approach to projective Riccati equations.
result Characterization of Riccati chain equations geometrically.
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48 results for “Riccati hierarchy”
Mixed superposition rules, i.e., functions describing the general solution of a system of first-order differential equations in terms of a generic family of particular solutions of first-order systems and some constants, are studied. The main achievement is a generalization of the celebrated Lie-Scheffers Theorem, char…
The study connects free subgroups in a specific group to hypermaps, deriving generating series and asymptotic formulas.
problem Counting and understanding free subgroups of a specific group and their conjugacy classes.
method Using a connection to hypermaps, deriving generating series and recurrence relations, and providing asymptotic formulas.
result The generating series for the numbers of free subgroups of finite index in the group is transcendental and provides non-linear recurrence relations.
Market makers use a new method to predict and respond to RFQs in the OTC market.
problem Predicting and managing RFQs in the OTC market with Hawkes kernels.
method Developed a hierarchy of Volterra-Riccati approximations for path-dependent control problems.
result The state-feedback Volterra-Riccati policy closely tracks the exact benchmark and improves inventory and P&L risk control.
Geometry of cross ratiomath.AP
Generalization of the cross ratio to polarizations of linear finite and infinite-dimensional spaces (in particular to Sato Grassmannian) is given and explored. This cross ratio appears to be a cocycle of the canonical (tautalogical) bundle over the Grassmannian with coefficients in the sheaf of its endomorphisms. Opera…
Affine connections linked to Riccati distributions on compact surfaces.
problem Understanding affine structures on complex compact surfaces.
method Established a correspondence between affine connections and Riccati distributions.
result One-to-one correspondence between affine structures and Riccati foliations on compact surfaces.
Paper derives Riccati equation for static spaces and proves its applications.
problem Deriving Riccati equation for static spaces.
method Proving splitting theorem and connectivity of conformal boundary.
result Establishes compactness of universal covering for static triples.
A new tontine design aims to protect longevity risk with non-indexed investments.
problem Pooling longevity risk with traditional methods.
method Non-indexed investments with negatively correlated returns to mortality.
result Mathematical proof of recovery schedule using a Riccati equation.
We study algebraic solutions of the Riccati equation over the field of rational functions , and over the elliptic function field .
Investigates mean-variance portfolio selection in non-Markovian markets.
problem Continuous-time Markowitz mean-variance portfolio selection in fake stationary affine Volterra models.
method Stochastic factor solution to a Riccati BSDE, deriving explicit solutions as multi-dimensional Riccati-Volterra equations.
result Analytical closed-form expressions for optimal portfolio policies and mean-variance efficient frontier.
Solves fractional Riccati equations for rough volatility models.
problem Fractional Riccati differential equations in financial models.
method Hybrid numerical algorithm using power series and Adams method.
result Hybrid algorithm is fast and stable, outperforming existing methods.
New techniques solve Riccati equations on 3D manifolds, finding 4th order metric obstructions.
problem Solving Riccati-type equations with algebraic constraints on 3D Riemannian manifolds.
method Real algebraic geometry techniques, focusing on connection coefficients and Hessian equations.
result Obstruction to solving Riccati equations has order 4 in metric coefficients.
New theory extends LQ control to non-exponential discount scenarios.
problem Time-inconsistent deterministic LQ control problems.
method Extended equivalent relationship to non-exponential discount functions, studied Riccati equation solvability.
result Existence and uniqueness of linear equilibrium for time-inconsistent LQ problem.
Investigates optimal investment strategies in financial markets with jumps.
problem Optimal portfolio selection for investors in multi-asset financial markets with jumps.
method Uses martingale optimality principle and Riccati backward stochastic differential equations with jumps.
result Derives semi-closed form optimal strategies and value function for Merton's problem.
A Mean-Field Control Problem of Optimal Portfolio Liquidation with Semimartingale Strategiesq-fin.MF
Study optimizes portfolio liquidation strategies with complex market impacts.
problem Optimizing portfolio liquidation with transient market impacts and self-exciting order flow.
method Mean-field control problem with semimartingale strategies, passing to continuous-time limit, and solving Riccati equations.
result Existence of optimal strategy with jumps only at start and end of trading period.
This paper optimizes portfolio selection for multivariate affine and quadratic Volterra models with rough volatilities.
problem Optimizing portfolio selection for multivariate models with rough volatilities and stochastic correlations.
method Investigates continuous-time Markowitz mean-variance problem for multivariate affine and quadratic Volterra models using Riccati backward stochastic differential equations (BSDEs).
result Derives explicit solutions for BSDEs in affine Volterra models and new analytic formulae for quadratic models.
Mapping Among Line Elementsmath.DG
Paper maps Hamiltonians and line elements in manifolds.
problem Mapping among generalized Hamiltonians and line elements.
method Constructing Calabi's Riemannian Line Elements and solving matrix Riccati equations.
result Analytical and exact solutions of mapping between manifolds.
Study solves HJB equations for time-inconsistent control problems.
problem Time-inconsistent deterministic linear quadratic control problems.
method Characterized solutions using Riccati equations with integral terms, proving uniqueness.
result Uniqueness of solutions to equilibrium HJB equations proved.
This paper deals with the question of analytic continuation of holonomy germs of holomorphic foliations. We prove that for a quasi-minimal Riccati foliation of the complex projective plane, any holonomy germ of the foliation between complex projective lines can be analytically continued along a generic Brownian path.
In this paper we develop some group theoretical methods which are shown to be very useful for a better understanding of the properties of the Riccati equation and we discuss some of its integrability conditions from a group theoretical perspective. The nonlinear superposition principle also arises in a simple way.
Paper solves Merton's portfolio problem in a non-Markovian, non-semimartingale model.
problem Merton's portfolio optimization in a fake stationary Volterra-Heston model.
method Stochastic factor solution to a Riccati BSDE, combined with martingale optimality principle.
result Derives semi-closed form optimal strategies and value function.
Alternative proofs for various inequalities on Riemannian manifolds.
problem Various functional inequalities on Riemannian manifolds.
method Generic functional inequality, Riccati pairs, solving Riccati-type ODE.
result Alternative proofs for multiple inequalities, including Hardy-type and Caccioppoli inequalities.
The paper solves a dynamic portfolio optimization problem using Riccati transformation.
problem Dynamic stochastic portfolio optimization involving expected and intertemporal utilities.
method Solving a fully nonlinear HJB equation through Riccati transformation into a quasi-linear parabolic equation.
result The numerical method based on semi-implicit scheme converges at second order.
Expanding the rough Heston model in q-fin.MF
Expanding the rough Heston model in
problem Analyzing the dependence of the fractional Riccati equation on the Hurst parameter
method Deriving a Taylor expansion of the Riccati solution in
result Local uniform convergence and analyticity of the fractional Riccati solution
It has been recently shown that rough volatility models, where the volatility is driven by a fractional Brownian motion with small Hurst parameter, provide very relevant dynamics in order to reproduce the behavior of both historical and implied volatilities. However, due to the non-Markovian nature of the fractional Br…
The paper studies Fourier-Laplace transforms in polynomial OU volatility models for option pricing.
problem Calibrating and pricing options in polynomial Ornstein-Uhlenbeck volatility models.
method Analyzes Fourier-Laplace transforms, connects to Riccati equations, and develops numerical schemes.
result Establishes existence and solution for Riccati equations and provides efficient numerical methods.
Affine forward variance modelsq-fin.MF
Introduces AFV models for variance, including Heston and rough Heston models.
problem Models for variance in financial markets.
method Characterizes AFV models with affine cumulant generating functions and convolution Riccati equations.
result AFV models can be high-frequency limits of AFI models driven by jump processes.
We generalize the classical Lie results on a basis of differential invariants for a one-parameter group of local transformations to the case of arbitrary number of independent and dependent variables. It is proved that if universal invariant of a one-parameter group is known then a complete set of functionally independ…
Researchers developed volume comparison theorems in Finsler spacetimes.
problem Volume comparison in Finsler spacetimes with specific curvature conditions.
method Riccati equation techniques applied to -dimensional Lorentz--Finsler manifolds.
result Established volume comparison theorems for standard sets in Lorentzian volumes (SCLVs).
Solvability of Differential Riccati Equations and Applications to Algorithmic Trading with Signalsq-fin.TR
Study solves DREs for trading strategies using signals and past prices.
problem Solving DREs for optimal trading strategies.
method Analyzes DREs with indefinite matrix coefficients and applies to trading problems.
result Derives optimal trading strategies using signals and past prices.
We propose two methods to obtain exact solutions for the Almgren-Chriss model about optimal execution of portfolio transactions. In the first method we rewrite the Almgren-Chriss equation and find two exact solutions. In the second method, employing a general reparametrized time, we show that the Almgren-Chriss equatio…
Researchers derive an explicit Laplace transform for integrated Volterra Wishart process.
problem Modeling and pricing financial instruments with complex covariance structures.
method Explicit expression for conditional Laplace transform of integrated Volterra Wishart process, linking to matrix Riccati equations.
result Derivation of Laplace transform for a special case of convolution kernel, leading to efficient pricing methods.
The paper defines and studies the geometric mean for tensors and its associated Riemannian geometry.
problem Defining and studying the geometric mean for tensors.
method Generalized geometric mean for tensors using T-product, verified properties, and investigated Riemannian manifold.
result Geometric mean of T-positive definite tensors is a unique solution of algebraic Riccati tensor equations and a midpoint of geodesics.
A new model minimizes investment risk at multiple time points.
problem Minimizing risk in investment portfolios with multiple stopping points.
method Developed a multi-time state mean-variance model using Riccati equations.
result Optimal investment strategies can be derived from a sequence of Riccati equations.
New approach connects UQ in SciML to viscous HJ PDEs for efficient uncertainty quantification.
problem Challenges in interpretability and expensive training procedures in UQ for SciML.
method Established connection between Bayesian inference and viscous HJ PDEs, developed Riccati-based methodology.
result Efficiently updates model predictions without retraining or data access, suitable for real-time inferences.
Investigates Merton's portfolio problem in a rough stochastic environment with Volterra Heston model.
problem Optimizing investment strategies in a non-Markovian, non-semimartingale stochastic environment.
method Solves the portfolio optimization problem using the martingale optimality principle and auxiliary random process.
result Derives semi-closed form solutions for optimal strategies under power and exponential utilities.
We provide explicit solutions of certain forward-backward stochastic differential equations (FBSDEs) with quadratic growth. These particular FBSDEs are associated with quadratic term structure models of interest rates and characterize the zero-coupon bond price. The results of this paper are naturally related to simila…
Construct geometric interpretation of Heston model using group quantization.
problem Geometric interpretation of Heston model
method Lifted local Lie groupoid formulation
result Geometric interpretation of Heston pricing operator and Riccati equations
Study of affine processes without stochastic continuity assumption.
problem Time-inhomogeneous affine processes with unpredictable jumps.
method Developed a general theory of finite dimensional affine semimartingales under weak assumptions.
result Affine form of semimartingale characteristics and solutions to Riccati equations.
Constructs integrable hierarchies for generalized Frobenius manifolds with non-flat unity.
problem Integrable hierarchies for generalized Frobenius manifolds with non-flat unity.
method Constructs a bihamiltonian integrable hierarchy of hydrodynamic type.
result Integrable hierarchy possesses Virasoro symmetries and a tau structure.
New method solves stochastic control problems with delays using deep learning.
problem Stochastic control problems with delayed control in drift and diffusion.
method Characterization via Riccati PDEs and deep learning scheme.
result Illustrates effect of delay on Markowitz portfolio allocation problem.
Hawking-Penrose theorem holds for -metrics, with weak conditions.
problem Extending singularity theorems to less smooth metrics.
method Formulated weak conditions for -metrics, analyzed matrix Riccati equation.
result Causal geodesics become non-maximizing under weak conditions.
Investigates portfolio selection under rough volatility model, showing quadratic efficient frontier.
problem Mean-variance portfolio selection under rough volatility models.
method Constructs an auxiliary stochastic process to solve Riccati-Volterra equation for optimal strategy.
result MV efficient frontier is quadratic, influenced by roughness and volatility of volatility.
Study of J-Hermitian matrices and geometric mean definition.
problem Understanding the cone of J-Hermitian matrices and its geometric mean.
method Analysis of the cone structure, Riemannian structure, and definition of J-geometric mean.
result Uniquely characterized J-geometric mean defined as a solution to a Riccati-type equation.
Study identifies pitfalls in assessing hierarchies for multi-class classification.
problem Lack of understanding in selecting hierarchies for multi-class classification.
method Analyzed and compared popular approaches to extracting hierarchies.
result Hierarchy quality becomes irrelevant when using powerful classifiers.
Super tau-covers extend bihamiltonian hierarchies' symmetries.
problem Extending symmetries of bihamiltonian hierarchies.
method Constructing super tau-covers for bihamiltonian integrable hierarchies.
result Symmetries of bihamiltonian hierarchies extended to super tau-covers.
Hydrodynamic hierarchy deformed using conservation laws.
problem Deforming a hydrodynamic hierarchy with non-vanishing Nijenhuis torsion.
method Using a chain of conservation laws to deform the hierarchy.
result The resulting hierarchy has non-vanishing Nijenhuis torsion but vanishing Haantjes tensor.
New hierarchy for a special group type.
problem Classifying relatively hyperbolic virtually special groups.
method Constructing a new virtual quasiconvex hierarchy.
result Generalized Malnormal Special Quotient Theorem.