Optimal investment under behavioural criteria -- a dual approach

We consider a discrete-time, generically incomplete market model and a behavioural investor with power-like utility and distortion functions. The existence of optimal strategies in this setting has been shown in a previous paper under certain conditions on the parameters of these power functions. In the present paper we prove the existence of optimal strategies under a different set of conditions on the parameters, identical to the ones which were shown to be necessary and sufficient in the Black-Scholes model. Although there exists no natural dual problem for optimisation under behavioural criteria (due to the lack of concavity), we will rely on techniques based on the usual duality between attainable contingent claims and equivalent martingale measures.Comment: Forthcoming in Banach Center Publications. Some errors have been corrected, in particular in Assumption 2.3

Optimal Investment under Behavioral Criteria in Incomplete Diffusion Market Models

The existence of optimal strategies is established for a behavioral investor in certain incomplete continuous time market models

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

Postoperative interictal spikes during sleep contralateral to the operated side is associated with unfavourable surgical outcome in patients with preoperative bitemporal spikes

AbstractPurpose: To correlate the persistence of contralateral spikes during sleep after unilateral surgery with seizure outcome in a temporal lobe epilepsy (TLE) population and to test the existing hypotheses about the origin of the contralateral spikes in temporal lobe epilepsy. Methods: In the 19 patients selected for this study unilateral temporal lobe surgery was performed. To investigate the course of bilateral interictal epileptiform discharges observed before surgery in awake or sleep over the temporal lobe contralateral to surgery, 24h mobile 12 channel EEG recording was performed at minimum two, in average 4.6 (2–10) years after the surgery. Results: The association of postoperative contralateral spikes and non-seizure free outcome was highly significant. The existence of unilateral pathology before surgery was highly predictive for good outcome and disappearance of contralateral spikes. The association between good seizure outcome, disappearance of contralateral spikes and the existence of unilateral pathology before surgery was also significant. Our data partially satisfies the expectations of both the “seizure induced” and mirror type secondary epileptogenesis hypotheses concerning origin of contralateral spikes, but were not completely congruent with either of them. Conclusions: Unfavourable surgical outcome in a temporal lobe epilepsy group with preoperative independent bilateral interictal spikes was associated with the persistence of postoperative contralateral spikes and lack of unilateral pathology. Compared with seizure outcome the presence/absence and distribution of postoperative interictal spikes in NREM sleep not entirely fit to the predictions of existing secondary epileptogenesis hypotheses

A note on arbitrage in term structure

Arbitrage, Term structure, Large financial markets, Kakutani theorem, Gaussian random variables, 91B28, 60G42, G10, G12,

Clinical differences in patients with unilateral hippocampal sclerosis and unitemporal or bitemporal epileptiform discharges

AbstractPurpose: To investigate factors determining the presence of bilateral interictal epileptiform discharges (IEDs) in temporal lobe epilepsy (TLE) with unilateral hippocampal sclerosis (HS).Methods: We analysed data of 243 TLE patients with unilateral HS who had long-term video-EEG. Eighty-one patients (33%) had bitemporal IEDs.Results: We categorised patients into a unilateral group (UG), a bilateral group (BG) according to presence of bitemporal IEDs. We found no difference between UG and BG regarding epilepsy duration, secondarily generalised seizures, and history of febrile seizures. Mean seizure frequency was significantly higher in the BG (UG: 7.7±14.7 seizures/month; BG: 13±35 seizures/month, P=0.01). We found a significant correlation between late epilepsy onset and the presence of bitemporal IEDs. The mean age at epilepsy onset in UG was 10.1±7.9 years, while in BG it was 13±9.2 years (P=0.02).Conclusions: The traditional concept of the evolution of mirror focus cannot apply for humans because the duration of epilepsy does not influence the evolution of bitemporal IEDs. Other factors, i.e. age at onset and seizure frequency may play a role in this process. The association between the higher seizure frequency and mirror foci indicates that the development of mirror focus depends on seizures and not on a progressive ‘interictal’ epileptogenesis