Extends utility maximization theory for infinite horizons without strong no-arbitrage assumptions.
problem Maximizing lifetime utility from wealth over an infinite horizon.
method Develops a duality theory using deflators and supermartingale properties, extending previous work.
result Establishes a strong duality theorem for infinite horizon utility maximization under minimal no-arbitrage assumptions.
Study resolves duality gap in optimal consumption with random income termination.
problem Optimal consumption in a market with randomly terminating income.
method Established rigorous duality theory using supermartingale deflators.
result Closed duality gap and characterized optimal wealth process.
Study optimal portfolio management with periodic evaluations in stochastic models, considering convex constraints.
problem Optimal portfolio management under ratio-type periodic evaluations in stochastic factor models with convex trading constraints.
method Transformed infinite horizon optimal control problem into an auxiliary terminal wealth optimization problem. Introduced an auxiliary unconstrained optimization problem in a modified market model. Used martingale duality approach to establish dual minimizer and optimal unconstrained wealth process.
result Derived and verified the optimal constrained portfolio process for the original problem over an infinite horizon.
We study the Immediate Exchange model, recently introduced by Heinsalu and Patriarca [Eur. Phys. J. B 87: 170 (2014)], who showed by simulations that the wealth distribution in this model converges to a Gamma distribution with shape parameter 2. Here we justify this conclusion analytically, in the infinite-population…
We solve optimal consumption in a market with bounded risk.
problem Optimal consumption in a semimartingale market with bounded risk.
method Use supermartingale deflators to prove strong duality.
result Strong duality and complete characterisation of optimal consumption.
We study the finite-size effects in some scaling systems, and show that the finite number of agents N leads to a cut-off in the upper value of the Pareto law for the relative individual wealth. The exponent α of the Pareto law obtained in stochastic multiplicative market models is crucially affected by the fact that …
We consider an arbitrage-free, discrete time and frictionless market. We prove that an investor maximising the expected utility of her terminal wealth can always find an optimal investment strategy provided that her dissatisfaction of infinite losses is infinite and her utility function is non-decreasing, continuous an…
Optimal strategies are found for a repeated betting game using diffusion approximation.
problem Finding optimal strategies for a repeated betting game with i.i.d. outcomes.
method Constructing a diffusion approximation of the repeated game and analyzing the wealth share process.
result Necessary and sufficient conditions for the wealth share process to be transient or recurrent are derived.
We consider a financial market model driven by an R^n-valued Gaussian process with stationary increments which is different from Brownian motion. This driving noise process consists of n independent components, and each component has memory described by two parameters. For this market model, we explicitly solve optim…
New tontine model with transaction costs for retirees.
problem Maximizing consumption and bequest utilities for retirees.
method Formulated as a stochastic and impulse control problem, characterized by viscosity solutions.
result V-shaped transaction region with two stages: smoothing and gambling.
This paper optimizes portfolio management in incomplete markets with stochastic factors, considering periodic wealth evaluations.
problem Optimizing portfolio performance in an incomplete market model with stochastic factors and periodic wealth evaluations.
method Developed a martingale duality approach to find optimal portfolio processes and dual minimizers.
result Established the existence of optimal portfolio processes and identified dual minimizers as the 'least favorable' market completion.
Using a model based on generalised Lotka Volterra dynamics together with some recent results for the solution of generalised Langevin equations, we show that the equilibrium solution for the probability distribution of wealth has two characteristic regimes. For large values of wealth it takes the form of a Pareto style…
Paper proposes financial schemes that exploit the Axiom of Choice for quick gains.
problem Financial quick gains through non-degenerate price paths.
method Trading schemes based on the Axiom of Choice, considering continuous and positive price paths.
result Schemes can lead to infinite wealth under certain conditions, but are impractical due to the Axiom of Choice.
We develop a polynomial method to optimize trading in markets with transaction costs.
problem Optimizing trading strategies in markets with proportional transaction costs.
method Polynomial approximation of the residual value function to determine optimal trading strategies.
result Identify the trade-off between trading frequency and trade sizes for satisfactory agreement with theoretically optimal strategies.
We investigate the relation between economic growth and equality in a modified version of the agent-based asset exchange model (AEM). The modified model is a driven system that for a range of parameter space is effectively ergodic in the limit of an infinite system. We find that the belief that "a rising tide lifts all…
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 fluctuations. The consumption rate is subject to an upper bound constraint which linea…
Survival strategies in a market with self-determined prices are closely tied to log-optimal investment.
problem Survival of wealth in a market with endogenous prices.
method Assume only one's actions affect prices, use log-optimal strategy, disregard actual prices.
result Survival strategies are asymptotically close to log-optimal strategies.
Investor optimizes wealth in a market with non-traded endowment, deriving expansions up to second order.
problem Optimizing wealth in an incomplete financial market with a non-traded endowment.
method Duality techniques and Kunita-Watanabe projections for deriving expansions up to second order.
result Derives expansions of the primal value function and optimal wealth process up to second order with respect to the non-traded endowment units.
Model compares altruism and individualism in wealth dynamics.
problem Comparing altruism and individualism in wealth dynamics.
method Minimalist dynamical model of wealth evolution and sharing among N agents.
result Altruism leads to more global median wealth at early times but individualists accumulate most wealth in the long run.
A new method uses BSDEs to solve optimal reinsurance under partial information.
problem Maximizing wealth in insurance with partial loss information.
method Backward Stochastic Differential Equations (BSDEs) for infinite-dimensional filtering problem.
result Optimal reinsurance strategy found via BSDE solution.
We model a closed economic system with interactions that generates the features of empirical wealth distribution across all wealth brackets, namely a Gibbsian trend in the lower and middle wealth range and a Pareto trend in the higher range, by simply limiting the an agents' interaction to only agents with nearly the s…
Combines absolute and relative wealth in portfolio optimization with power utility functions.
problem Optimizing portfolios with both absolute and relative wealth considerations.
method Integrates power utility functions for absolute and relative wealth, considering multiple benchmarks.
result Obtains an explicit solution for portfolio optimization combining absolute and relative wealth.
Optimal investment and consumption model with habit formation constraint.
problem Formulating an optimal investment and consumption model with habit formation constraint.
method Formulated an infinite-horizon optimal investment and consumption problem with habit formation model, derived explicit policies, and analyzed the system of differential equations.
result Optimal investment and consumption policies derived explicitly, showing different consumption and investment strategies based on habit formation level.
Financial investment returns lead to growing wealth inequality.
problem Recent rise in wealth inequality in active financial markets.
method Minimalist modelling strategy combining financial markets, wealth accumulation, and compound interest.
result Accumulated financial investment returns cause ever-increasing wealth concentration and inequality.
We analyze wealth condensation for a wide class of stochastic economy models on the basis of the economic analog of thermodynamic potentials, termed transfer potentials. The economy model is based on three common transfers modes of wealth: random transfer, profit proportional to wealth and motivation of poor agents to …
New proof shows local wealth condensation in economic models with biases.
problem Economic models with biases leading to wealth condensation.
method Elementary proof based on properties of wealth distributions.
result Local wealth condensation observed in models with wealth or poverty advantages.
Short proof shows wealth condensation in trading model.
problem Proving wealth condensation in trading model.
method Short proof extending to modified model with wealth advantage.
result Wealth condensation occurs almost surely in modified model.
The logistic equation describes wealth condensation in a WAA-enhanced asset exchange model.
problem Analyzing wealth condensation in asset exchange models with wealth advantage.
method Introduced a continuous wealth advantage bias in the YSM, derived a logistic equation for the condensed wealth.
result Condensation of wealth follows a logistic equation in time.
Reproductive success and survival are influenced by wealth in human populations. Wealth is transmitted to offsprings and strategies of transmission vary over time and among populations, the main variation being how equally wealth is transmitted to children. Here we propose a model where we simulate both the dynamics of…
The so-called "Yard-Sale Model" of wealth distribution posits that wealth is transferred between economic agents as a result of transactions whose size is proportional to the wealth of the less wealthy agent. In recent work [B.M. Boghosian, "Kinetics of Wealth and the Pareto Law," {\it Phys. Rev. E} {\bf 89} (2014) 042…
Paper proposes a new framework for combining investment strategies without market-specific assumptions.
problem Lack of a distribution-free and consistent preference framework for decision-making in combining investment strategies.
method Introduces a novel framework for decision-making in combining strategies, free from market conditions and statistical assumptions.
result Proposed strategies outperform individual component strategies in long-term wealth accumulation, with small tradeoffs in Sharpe ratios.
Agent-based model for wealth distribution with negative wealth.
problem Modeling wealth distribution with negative wealth and validating against empirical data.
method Agent-based model, Fokker-Planck equation, numerical solution, inverse problem solving.
result Agreement with empirical data of an average error less than 0.16% over 27 years.
The paper analyzes optimal consumption with past spending maximum as a reference.
problem Optimal consumption with past spending maximum as a reference.
method Path-dependent exponential utility, Hamilton-Jacobi-Bellman (HJB) equation, dual transform, smooth-fit principle.
result Closed-form solutions for optimal investment and consumption strategies in each region.
Model shows who pays higher taxes affects wealth distribution.
problem Determining who should pay higher taxes to prevent wealth concentration.
method Dynamic agent model with random wealth multiplicative process and linear tax rate.
result Tax rate structure affects long-term wealth distribution.
Study explores how wealth dynamics change with preferential interactions in kinetic exchange models.
problem Investigate how preferential interactions affect wealth dynamics and distributions in kinetic exchange models.
method Conducted Monte Carlo simulations to explore two types of preferential interactions: one with random selection and another with wealth difference constraint.
result Emergence of quasi-oligarchic societies and segregation into economic classes observed in preferential interactions.
In this article we show that the payment flow of a linear tax on trading gains from a security with a semimartingale price process can be constructed for all càglàd and adapted trading strategies. It is characterized as the unique continuous extension of the tax payments for elementary strategies w.r.t. the convergence…
Model shows how investment traps wealth across generations.
problem Existence of wealth traps between social strata.
method Developed a model linking investment and intergenerational wealth.
result Proved a `rat race' theorem showing investment traps wealth.
Some general features of kinetic multi-agent models are reviewed, with particular attention to the relation between the agent saving propensities and the form of the equilibrium wealth distribution. The effect of a finite cutoff of the saving propensity distribution on the corresponding wealth distribution is studied. …
A wealth-process set is abstractly defined to consist of nonnegative càdlàg processes containing a strictly positive semimartingale and satisfying an intuitive re-balancing property. Under the condition of absence of arbitrage of the first kind, it is established that all wealth processes are semimartingales and that t…
Study finds Pareto distribution for wealth and income of Norway's richest individuals.
problem Analyzing wealth and income distribution of Norway's richest individuals.
method Empirical data from Norwegian tax office, using Pareto law.
result Robust mean Pareto exponents for income and wealth are approximately 2.3 and 1.5 respectively.
The subject of this paper is an optimal consumption/optimal portfolio problem with transaction costs and with multiple risky assets. In our model the transaction costs take a special form in that transaction costs on purchases of one of the risky assets (the endowed asset) are infinite, and transaction costs involving …
Analyzes how economic policies affect wealth distribution in Bitcoin token economy.
problem Impact of economic policies on wealth distribution in token economies.
method Eliminated noise in wealth distribution data using macroeconomic and microeconomic time series. Causality analysis between BIPs and wealth distribution data.
result Proposed a structure for economic policy taxonomy in token economies.
Inequality persists as wealth concentrates in a few agents.
problem Widening wealth gap in society.
method Modeling wealth exchanges and proposing regulatory policies.
result Simple policies can redistribute wealth and prevent inequality.
Study shows bifurcation in optimal retirement planning.
problem Optimal consumption and retirement planning model.
method Cobb-Douglas utility, simple model with wealth bifurcation.
result Critical wealth level leads to a continuum of retirement trajectories.
Modeling resource accumulation in a population game to explain wealth distribution.
problem Explaining the distribution of wealth in a population game.
method Modeling resource accumulation as a population game with Hawk-Dove interactions, analyzing fitness/wealth distribution and evolution over time.
result Long-run average fitness/wealth is non-monotonic with resource value, explaining the 'curse of riches'.
Bayesian investor learns unknown asset drift, trades mean-variance optimal portfolio, but policy is robust to observation model distortion.
problem Bayesian portfolio selection with observation model distortion
method Robust Bayesian portfolio selection
result Robust policy and its price are closed form, with price of robustness half the variance of the non-robust investor's loss.
A computational model for the distribution of wealth among the members of an ideal society is presented. It is determined that a realistic distribution of wealth depends upon two mechanisms: an asymmetric flux of wealth in trading transactions that advantages the poorer of the two traders and a non-stationary creation …
Study shows wealth distribution tails near criticality are not universal.
problem Understanding wealth distribution tails near criticality.
method Generalized affine wealth model with nonconstant redistribution.
result Exponential tail near criticality is not universal; depends on redistribution policy.