Related papers: Consumption processes and positively homogeneous p…
We propose martingale consumption as a natural, desirable consumption pattern for any given (proportional) investment strategy. The idea is to always adjust current consumption so as to achieve level expected future consumption under the…
The consumption function maps current wealth and the exogenous state to current consumption. We prove the existence and uniqueness of a consumption function when the agent has a preference for wealth. When the period utility functions are…
We prove that the consumption functions in optimal savings problems are asymptotically linear if the marginal utility is regularly varying. We also analytically characterize the asymptotic marginal propensities to consume (MPCs) out of…
Under the assumption of (positive) homogeneity (PH in the sequel) of the corresponding utility functions, we construct polynomial time algorithms for the weak separability, the collective consumption behavior and some related problems.…
The main objective of this paper is to develop a martingale-type solution to optimal consumption--investment choice problems ([Merton, 1969] and [Merton, 1971]) under time-varying incomplete preferences driven by externalities such as…
We consider a general discrete-time financial market with proportional transaction costs as in [Kabanov, Stricker and R\'{a}sonyi Finance and Stochastics 7 (2003) 403--411] and [Schachermayer Math. Finance 14 (2004) 19--48]. In addition to…
A continuous-time consumption-investment model with constraint is considered for a small investor whose decisions are the consumption rate and the allocation of wealth to a risk-free and a risky asset with logarithmic Brownian motion…
We provide a detailed characterization of the optimal consumption stream for the additive habit-forming utility maximization problem, in a framework of general discrete-time incomplete markets and random endowments. This characterization…
We consider a continuous-time game-theoretic model of an investment market with short-lived assets and endogenous asset prices. The first goal of the paper is to formulate a stochastic equation which determines wealth processes of investors…
We consider a discrete-time financial market model with finite time horizon and give conditions which guarantee the existence of an optimal strategy for the problem of maximizing expected terminal utility. Equivalent martingale measures are…
This paper considers the problem of consumption and investment in a financial market within a continuous time stochastic economy. The investor exhibits a change in the discount rate. The investment opportunities are a stock and a riskless…
We consider the problem of optimal consumption from labor income and investment in a general incomplete semimartingale market. The economic agent cannot borrow against future income, so the total wealth is required to be positive at (all or…
Empirical evidence suggests that the rich have higher propensity to save than do the poor. While this observation may appear to contradict the homotheticity of preferences, we theoretically show that that is not the case. Specifically, we…
We study the $\mathcal{L}_p$ induced gain of discrete-time linear switching systems with graph-constrained switching sequences. We first prove that, for stable systems in a minimal realization, for every $p \geq 1$, the $\mathcal{L}_p$-gain…
We consider a problem of an optimal consumption strategy on the infinite time horizon when the short-rate is a diffusion process. General existence and uniqueness theorem is illustrated by the Vasicek and so-called invariant interval…
We consider qualitative strategy synthesis for the formalism called consumption Markov decision processes. This formalism can model dynamics of an agents that operates under resource constraints in a stochastic environment. The presented…
Earlier we proposed the stochastic point process model, which reproduces a variety of self-affine time series exhibiting power spectral density S(f) scaling as power of the frequency f and derived a stochastic differential equation with the…
This paper studies the optimal consumption under the addictive habit formation preference in markets with transaction costs and unbounded random endowments. To model the proportional transaction costs, we adopt the Kabanov's multi-asset…
This paper studies the infinite-horizon optimal consumption with a path-dependent reference under exponential utility. The performance is measured by the difference between the nonnegative consumption rate and a fraction of the historical…
The choice of admissible trading strategies in mathematical modelling of financial markets is a delicate issue, going back to Harrison and Kreps (1979). In the context of optimal portfolio selection with expected utility preferences this…