Related papers: An equation for a time-dependent profit rate

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…

This paper re-examines the use of response time to infer problem complexity. It revisits a canonical Wald model of optimal stopping, taking signal-to-noise ratio as a measure of problem complexity. While choice quality is monotone in…

In this paper we propose a new way of proving the value of a firm that is currently producing a certain product and faces the option to exit the market. The problem of optimal exiting is an optimal stopping problem, that can be solved using…

The decision process requires information about the present state of the system, but in economy acquiring data and processing them is an expensive and time consuming process. Therefore the state of the system is measured and announced at…

This dissertation reports work where physics methods are applied to financial and economical problems. The first part studies stock market data (chapter 1 to 5). The second part is devoted to personal income in the USA (chapter 6). We first…

Forecasting technological progress is of great interest to engineers, policy makers, and private investors. Several models have been proposed for predicting technological improvement, but how well do these models perform? An early…

In their activity, the traders approximate the rate of return by integer multiples of a minimal one. Therefore, it can be regarded as a quantized variable. On the other hand, there is the impossibility of observing the rate of return and…

We study the problem of optimal long term portfolio selection with a view to beat a benchmark. Two kinds of objectives are considered. One concerns the probability of outperforming the benchmark and seeks either to minimise the decay rate…

This paper studies the income fluctuation problem with capital income risk (i.e., dispersion in the rate of return to wealth). Wealth returns and labor earnings are allowed to be serially correlated and mutually dependent. Rewards can be…

We investigate the dynamics of growth models in terms of dynamical system theory. We analyse some forms of knowledge and its influence on economic growth. We assume that the rate of change of knowledge depends on both the rate of change of…

We consider a second order linear evolution equation with a dissipative term multiplied by a time-dependent coefficient. Our aim is to design the coefficient in such a way that all solutions decay in time as fast as possible. We discover…

We investigate activities that have different periods of duration. We define the profit intensity as a measure of this economic category. The profit intensity in a repeated trading has a unique property of attaining its maximum at a fixed…

We consider the passage time problem for L\'evy processes, emphasising heavy tailed cases. Results are obtained under quite mild assumptions, namely, drift to $-\infty$ a.s. of the process, possibly at a linear rate (the finite mean case),…

We study the tradeoff between fundamental risk and time. A time-constrained agent has to solve a problem. She dynamically allocates effort between implementing a risky initial idea and exploring alternatives. Discovering an alternative…

We consider fractional diffusion equations and study the stability of the inverse problem of determining the time-dependent parameter in a source term or a coefficient of zero-th order term from observations of the solution at one point in…

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…

Response times contain information about economically relevant but unobserved variables like willingness to pay, preference intensity, quality, or happiness. We provide a general characterization of the properties of latent variables that…

We derive an equation for temporal difference learning from statistical principles. Specifically, we start with the variational principle and then bootstrap to produce an updating rule for discounted state value estimates. The resulting…

This paper analyzes how expectations of Transformative AI (TAI) affect current economic behavior by introducing a novel mechanism where automation redirects labor income from workers to those controlling AI systems, with the share of…

I prove that if markets are weak-form efficient, meaning current prices fully reflect all information available in past prices, then P = NP, meaning every computational problem whose solution can be verified in polynomial time can also be…