arXiv subjects

Adam Jonsson

Publications and source records attributed to Adam Jonsson.

6 recordsLinked to original sources

arXiv2023

On optimal control of reflected diffusions

We study a simple singular control problem for a Brownian motion with constant drift and variance reflected at the origin. Exerting control pushes the process towards the origin and generates a concave increasing state-dependent yield which is discounted at a fixed rate. The most interesting feature of the problem is that its solution can be more complicated than anticipated. Indeed, for some parameter values, the optimal policy involves two reflecting barriers and one repelling boundary, the action region being the union of two disjoint intervals. We also show that the apparent anomaly can be understood as involving a switch between two strategies with different risk profiles: The risk-neutral decision maker initially gambles on the more risky strategy, but lowers risk if this strategy underperforms.

math.PR↗

arXiv2021

Infinite utility: counterparts and ultimate locations

The locations problem in infinite ethics concerns the relative moral status of different categories of potential bearers of value, the primary examples of which are people and points in time. The challenge is to determine which category of value bearers are of ultimate moral significance: the ultimate locations, for short. This paper defends the view that the ultimate locations are 'people at times'. A person at a time is not a specific person, but the person born at a specific point in time (de dicto). The main conclusion of the paper is that the unsettling implications of the time- and person-centered approaches to infinite ethics can be avoided. Most notably, a broad class of worlds that person-centered views deem incomparable can be strictly ranked.

econ.TH↗

arXiv2018

A New Model for the Distribution of Observable Earthquake Magnitudes and Applications to $b$-value Estimation

The $b$-value in the Gutenberg-Richter (GR) law contains information that is essential for evaluating earthquake hazard and predicting the occurrence of large earthquakes. Estimates of $b$ are often based on seismic events whose magnitude exceed a certain threshold, the so called magnitude of completeness. Such estimates are sensitive to the choice of threshold and often ignore a substantial portion of available data. We present a general model for the distribution of observable earthquake magnitudes and an estimation procedure that takes all measurements into account. The model is obtained by generalizing previous probabilistic descriptions of sensor network limitations and by using a generalization of the GR law. We show that our model is flexible enough to handle spatio-temporal variations in the seismic environment and captures valuable information about sensor network coverage. We also show that the model leads to significantly improved $b$-value estimates compared with established methods relying on the magnitude of completeness.

physics.geo-ph↗

arXiv2017

An axiomatic approach to Markov decision processes

This paper presents an axiomatic approach to finite Markov decision processes where the discount rate is zero. One of the principal difficulties in the no discounting case is that, even if attention is restricted to stationary policies, a strong overtaking optimal policy need not exists. We provide preference foundations for two criteria that do admit optimal policies: $0$-discount optimality and average overtaking optimality. As a corollary of our results, we obtain conditions on a decision maker's preferences which ensure that an optimal policy exists. These results have implications for disciplines where stochastic dynamic programming problems arise, including automatic control, dynamic games, and economic development.

math.OC↗

arXiv2016

On g-functions for countable state subshifts

This note revisits the problem of finding necessary and sufficient conditions for a subshift to have a continuous g-function. Results obtained by Krieger (IMS Lecture Notes-Monograph Series, 48, 306--316, 2006) on finite alphabet subshifts are generalized to countable state subshifts.

math.DS↗

arXiv2015

Invariant sets for QMF functions

A quadrature mirror filter (QMF) function can be considered as the transition function for a Markov process on the unit interval. The QMF functions that generate scaling functions for multiresolution analyses are then distinguished by properties of their invariant sets. By characterizing these sets, we answer in the affirmative a question raised by Gundy (Notices Amer. Math. Soc. 57, 1094-1104, 2010).

math.PR↗