Non-concave utility maximisation on the positive real axis in discrete time

We treat a discrete-time asset allocation problem in an arbitrage-free, generically incomplete financial market, where the investor has a possibly non-concave utility function and wealth is restricted to remain non-negative. Under easily verifiable conditions, we establish the existence of optimal portfolios.Comment: 20 page

No-arbitrage in discrete-time markets with proportional transaction costs and general information structure

We discuss the no-arbitrage conditions in a general framework for discrete-time models of financial markets with proportional transaction costs and general information structure. We extend the results of Kabanov and al. (2002), Kabanov and al. (2003) and Schachermayer (2004) to the case where bid-ask spreads are not known with certainty. In the "no-friction" case, we retrieve the result of Kabanov and Stricker (2003)

Somatosensory phenomena elicited by electrical stimulation of hippocampus: Insight into the ictal network.

Up to 11% of patients with mesial temporal lobe epilepsy experience somatosensory auras, although these structures do not have any somatosensory physiological representation. We present the case of a patient with left mesial temporal lobe epilepsy who had somatosensory auras on the right side of the body. Stereo-EEG recording demonstrated seizure onset in the left mesial temporal structures, with propagation to the sensory cortices, when the patient experienced the somatosensory aura. Direct electrical stimulation of both the left amygdala and the hippocampus elicited the patient's habitual, somatosensory aura, with afterdischarges propagating to sensory cortices. These unusual responses to cortical stimulation suggest that in patients with epilepsy, aberrant neural networks are established, which have an essential role in ictogenesis

On stochastic gradient Langevin dynamics with dependent data streams in the logconcave case

We study the problem of sampling from a probability distribution π on Rd which has a density w.r.t. the Lebesgue measure known up to a normalization factor x→ e−U(x)/f Rd e−U(y) dy. We analyze a sampling method based on the Euler discretization of the Langevin stochastic differential equations under the assumptions that the potential U is continuously differentiable, ∇U is Lipschitz, and U is strongly concave. We focus on the case where the gradient of the log-density cannot be directly computed but unbiased estimates of the gradient from possibly dependent observations are available. This setting can be seen as a combination of a stochastic approximation (here stochastic gradient) type algorithms with discretized Langevin dynamics. We obtain an upper bound of the Wasserstein-2 distance between the law of the iterates of this algorithm and the target distribution π with constants depending explicitly on the Lipschitz and strong convexity constants of the potential and the dimension of the space. Finally, under weaker assumptions on U and its gradient but in the presence of independent observations, we obtain analogous results in Wasserstein-2 distance. © 2021 ISI/B

ISSN: 1083-589X ELECTRONIC COMMUNICATIONS

Continuous-time portfolio optimisation for a behavioural investor with bounded utility on gain

On stochastic gradient Langevin dynamics with dependent data streams in the logconcave case

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