Estimates returns for dollar cost averaging using geometric Brownian motion.
problem Estimating returns for dollar cost averaging investing strategy.
method Uses geometric Brownian motion and log-Normal distribution to construct a lower bound for returns. Computes parameters recursively and in closed form for dollar cost averaging. Compares to lump sum investing for matching wealth distributions.
result Probability of negative returns is less than 2.5% for 40 years of annual dollar cost averaging.
The higher-end tail of the wealth distribution in India is studied using recently published lists of the wealth of richest Indians between the years 2002-4. The resulting rank distribution seems to imply a power-law tail for the wealth distribution, with a Pareto exponent between 0.81 and 0.92 (depending on the year un…
The paper analyzes how wealth affects investment strategies in incomplete markets.
problem Investment strategies in markets with incomplete information.
method Developed a five-component decomposition for optimal portfolio choice, solved explicitly for HARA utility and nonrandom interest rate, and used a stochastic volatility model for US equity data.
result Demonstrated the impacts of wealth-dependent utilities on optimal portfolio allocation, including cycle-dependence and hysteresis effect.
Model shows wealth taxes can cause sudden emigration waves, impacting GDP.
problem Estimating the economic impact of wealth taxes on emigration.
method Developed a social contagion model with tipping-point dynamics, embedded in Fokker-Planck framework.
result Micro-to-macro extrapolation requires five conditions to hold, violating each.
We present a detailed numerical analysis of the modified version of a conservative self-organized extremal model introduced by Pianegonda et. al. for the distribution of wealth of the people in a society. Here the trading process has been modified by the stochastic bipartite trading rule. More specifically in a trade o…
Upper bound on withdrawal success for geometric Levy alpha-stable wealth process.
problem Estimating the probability of completing a withdrawal schedule.
method Constructing a log-Levy alpha-stable lower bound and applying it to a schedule of withdrawals.
result Necessary conditions on initial investment and parameters for a 95% confidence of completing k withdrawals. 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.
Study estimates Medallion's compounded return before fees at 31.8%.
problem Incorrectly using yearly returns for compounding leads to overestimation of fund performance.
method Used fund sizes and trading profits to estimate compounded return; used manager's wealth as proxy for Simons.
result Annualized compounded return of Medallion before fees is likely under 35%
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.
We consider the estimation of the multi-period optimal portfolio obtained by maximizing an exponential utility. Employing Jeffreys' non-informative prior and the conjugate informative prior, we derive stochastic representations for the optimal portfolio weights at each time point of portfolio reallocation. This provide…
I show that if the capital accumulation dynamics is stochastic a new term, in addition to that given by accounting prices, has to be introduced in order to derive a correct estimate of the genuine wealth of an economy. In a simple model with multiplicative accumulation dynamics I show that: 1) the value function is alw…
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.
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…
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.
Statistical mechanics explains income and wealth distribution in developed economies.
problem Understanding the distribution of income and wealth in developed economies.
method Derive the distribution from firm dynamics using maximum entropy and mixture aggregation.
result Derive the robust two-class structure of income and wealth distribution.
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…
Wealth inequality is an important matter for economic theory and policy. Ongoing debates have been discussing recent rise in wealth inequality in connection with recent development of active financial markets around the world. Existing literature on wealth distribution connects the origins of wealth inequality with a v…
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.
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.
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 …
How do individuals accumulate wealth as they interact economically? We outline the consequences of a simple microscopic model in which repeated pairwise exchanges of assets between individuals build the wealth distribution of a population. This distribution is determined for generic exchange rules --- transactions that…
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.
Optimizes fund manager's wealth with partial information on market risk.
problem Maximizing wealth with incomplete information about market risk.
method Formulated as optimization under partial information, solved via martingale method and concavification.
result Shows how learning about market risk affects optimal investment strategy.
Almost universally, wealth is not distributed uniformly within societies or economies. Even though wealth data have been collected in various forms for centuries, the origins for the observed wealth-disparity and social inequality are not yet fully understood. Especially the impact and connections of human behavior on …
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…
Study extends wealth tax neutrality framework to heterogeneous investors.
problem Analyzing wealth tax neutrality in populations with varying return-generating ability.
method Extended Fokker-Planck framework to heterogeneous investors, deriving extended Fokker-Planck equation.
result Proportional wealth tax no longer neutral due to varying return-generating ability, leading to different real incidence and wealth distribution changes.
Pareto law, which states that wealth distribution in societies have a power-law tail, has been a subject of intensive investigations in statistical physics community. Several models have been employed to explain this behavior. However, most of the agent based models assume the conservation of number of agents and wealt…
We investigate the wealth evolution in a system of agents that exchange wealth through a disordered network in presence of an additive stochastic Gaussian noise. We show that the resulting wealth distribution is shaped by the degree distribution of the underlying network and in particular we verify that scale free netw…
We reformulate wealth taxation using Fokker-Planck equations to ensure tax neutrality.
problem Ensuring tax neutrality in wealth taxation frameworks.
method Reformulating the neutral wealth tax framework using stochastic dynamics and statistical physics, specifically Fokker-Planck equations.
result The framework clarifies when wealth taxation is a benign rescaling of dynamics and when it introduces new physics.
We review some aspects, especially those we can tackle analytically, of a minimal model of closed economy analogous to the kinetic theory model of ideal gases where the agents exchange wealth amongst themselves such that the total wealth is conserved, and each individual agent saves a fraction (0 < lambda < 1) of wealt…
We study the model of interacting agents proposed by Chatterjee et al that allows agents to both save and exchange wealth. Closed equations for the wealth distribution are developed using a mean field approximation. We show that when all agents have the same fixed savings propensity, subject to certain well defined app…
An important class of economic models involve agents whose wealth changes due to transactions with other agents. Several authors have pointed out an analogy with kinetic theory, which describes molecules whose momentum and energy changes due to interactions with other molecules. We pursue this analogy and derive a Bolt…
Continuous-time mean-variance portfolio selection model with nonlinear wealth equations and bankruptcy prohibition is investigated by the dual method. A necessary and sufficient condition which the optimal terminal wealth satisfies is obtained through a terminal perturbation technique. It is also shown that the optimal…
The addition of wealth-attained advantage (WAA) to the Yard-Sale Model (YSM) of asset exchange has been demonstrated to induce wealth condensation. In a model of WAA for which the bias is a continuous function of the wealth difference of the transacting agents, the condensation was shown to arise from a second-order ph…
We discuss a Pareto macro-economy (a) in a closed system with fixed total wealth and (b) in an open system with average mean wealth and compare our results to a similar analysis in a super-open system (c) with unbounded wealth. Wealth condensation takes place in the social phase for closed and open economies, while it …
The accumulation of individual fitness or wealth is modelled as a population game in which pairs of individuals are recurrently and randomly matched to play a game over a resource. In addition, all individuals have random access to a constant background resource, and their fitness or wealth depreciates over time. For b…
Unbiased wealth exchanges always lead to inequality.
problem Understanding wealth distribution in unbiased binary exchange systems.
method Analytical demonstration of unbiased binary exchanges leading to perfect inequality.
result Any system driven by unbiased binary exchanges will reach perfect inequality and zero mobility.
Voluntary insurance contracts constitute a puzzle because they increase the expectation value of one party's wealth, whereas both parties must sign for such contracts to exist. Classically, the puzzle is resolved by introducing non-linear utility functions, which encode asymmetric risk preferences; or by assuming the p…
Income and wealth distribution affect stability of a society to a large extent and high inequality affects it negatively. Moreover, in the case of developed countries, recently has been proven that inequality is closely related to all negative phenomena affecting society. So far, Econophysics papers tried to analyse in…
The inequality of wealth distribution is a universal phenomenon in the civilized nations, and it is often imputed to the Matthew effect, that is, the rich get richer and the poor get poorer. Some philosophers unjustified this phenomenon and tried to put the human civilization upon the evenness of wealth. Noticing the f…
Study Nash equilibrium in market with relative wealth concerns under partial information and heterogeneous priors.
problem Analyzing Nash equilibrium in a market with unobservable return rates and heterogeneous priors.
method Established a Nash equilibrium through a separation result and martingale argument. Used fully-coupled linear FBSDEs and deep neural networks for numerical computation.
result Investment strategies under relative wealth concerns exhibit a herd effect, with accurate prior estimators leading the market.
A financial market model with general semimartingale asset-price processes and where agents can only trade using no-short-sales strategies is considered. We show that wealth processes using continuous trading can be approximated very closely by wealth processes using simple combinations of buy-and-hold trading. This ap…