Weak equilibria for time-inconsistent control: with applications to investment-withdrawal decisions

This paper considers time-inconsistent problems when control and stopping strategies are required to be made simultaneously (called stopping control problems by us). We first formulate the timeinconsistent stopping control problems under general multi-dimensional controlled diffusion model and propose a formal definition of their equilibria. We show that an admissible pair $(\hat{u},C)$ of controlstopping policy is equilibrium if and only if the auxiliary function associated with it solves the extended HJB system, providing a methodology to verify or exclude equilibrium solutions. We provide several examples to illustrate applications to mathematical finance and control theory. For a problem whose reward function endogenously depends on the current wealth, the equilibrium is explicitly obtained. For another model with a non-exponential discount, we prove that any constant proportion strategy can not be equilibrium. We further show that general non-constant equilibrium exists and is described by singular boundary value problems. This example shows that considering our combined problems is essentially different from investigating them separately. In the end, we also provide a two-dimensional example with a hyperbolic discount

Equilibria for Time-inconsistent Singular Control Problems

We study a time-inconsistent singular control problem originating from irreversible reinsurance decisions with non-exponential discount. Novel definitions of weak and strong equilibria for time-inconsistent singular control problems are introduced. For the problem with non-exponential discount, both sufficient and necessary conditions are derived, providing a thorough mathematical characterization of both equilibria. In particular, the weak equilibrium can be characterized by an extended HJB system, which is a coupled system of non-local parabolic equations with free boundaries. Finally, by showing the existence of classical solutions to the extended HJB system, the existence of weak equilibrium is established under some additional assumptions

Consumption-investment decisions with endogenous reference point and drawdown constraint

We propose a consumption-investment decision model where past consumption peak $h$ plays a crucial role. There are two important consumption levels: the lowest constrained level and a reference level, at which the risk aversion in terms of consumption rate is changed. We solve this stochastic control problem and derive the optimal value function, optimal consumption plan, and optimal investment strategy in semi-explicit forms. We find five important thresholds of wealth, all as functions of $h$, and most of them are implicit nonlinear functions. As can be seen from numerical results, this intuitive and simple model has significant economic implications and there are at least three important predictions: the marginal propensity to consume out of wealth is generally decreasing in wealth but can be increasing with an intermediate level of wealth; the implied relative risk aversion is a smile in wealth; the welfare of the poor is more vulnerable to wealth shocks than the wealthy

Dynamic portfolio selection for nonlinear law-dependent preferences

This paper addresses the portfolio selection problem for nonlinear law-dependent preferences in continuous time, which inherently exhibit time inconsistency. Employing the method of stochastic maximum principle, we establish verification theorems for equilibrium strategies, accommodating both random market coefficients and incomplete markets. We derive the first-order condition (FOC) for the equilibrium strategies, using a notion of functional derivatives with respect to probability distributions. Then, with the help of the FOC we obtain the equilibrium strategies in closed form for two classes of implicitly defined preferences: CRRA and CARA betweenness preferences, with deterministic market coefficients. Finally, to show applications of our theoretical results to problems with random market coefficients, we examine the weighted utility. We reveal that the equilibrium strategy can be described by a coupled system of Quadratic Backward Stochastic Differential Equations (QBSDEs). The well-posedness of this system is generally open but is established under the special structures of our problem

Phenotypic Characterization of Transgenic Mice Overexpressing Neuregulin-1

BACKGROUND: Neuregulin-1 (NRG1) is one of the susceptibility genes for schizophrenia and implicated in the neurotrophic regulation of GABAergic and dopaminergic neurons, myelination, and NMDA receptor function. Postmortem studies often indicate a pathologic association of increased NRG1 expression or signaling with this illness. However, the psychobehavioral implication of NRG1 signaling has mainly been investigated using hypomorphic mutant mice for individual NRG1 splice variants. METHODOLOGY/PRINCIPAL FINDINGS: To assess the behavioral impact of hyper NRG1 signaling, we generated and analyzed two independent mouse transgenic (Tg) lines carrying the transgene of green fluorescent protein (GFP)-tagged type-1 NRG1 cDNA. The promoter of elongation-factor 1α gene drove ubiquitous expression of GFP-tagged NRG1 in the whole brain. As compared to control littermates, both heterozygous NRG1-Tg lines showed increased locomotor activity, a nonsignificant trend toward decreasing prepulse inhibition, and decreased context-dependent fear learning but exhibited normal levels of tone-dependent learning. In addition, social interaction scores in both Tg lines were reduced in an isolation-induced resident-intruder test. There were also phenotypic increases in a GABAergic marker (parvalbumin) as well as in myelination markers (myelin basic protein and 2',3'-cyclic nucleotide 3'-phosphodiesterase) in their frontal cortex, indicating the authenticity of NRG1 hyper-signaling, although there were marked decreases in tyrosine hydroxylase levels and dopamine content in the hippocampus. CONCLUSIONS: These findings suggest that aberrant hyper-signals of NRG1 also disrupt various cognitive and behavioral processes. Thus, neuropathological implication of hyper NRG1 signaling in psychiatric diseases should be evaluated with further experimentation

Potential of Core-Collapse Supernova Neutrino Detection at JUNO

JUNO is an underground neutrino observatory under construction in Jiangmen, China. It uses 20kton liquid scintillator as target, which enables it to detect supernova burst neutrinos of a large statistics for the next galactic core-collapse supernova (CCSN) and also pre-supernova neutrinos from the nearby CCSN progenitors. All flavors of supernova burst neutrinos can be detected by JUNO via several interaction channels, including inverse beta decay, elastic scattering on electron and proton, interactions on C12 nuclei, etc. This retains the possibility for JUNO to reconstruct the energy spectra of supernova burst neutrinos of all flavors. The real time monitoring systems based on FPGA and DAQ are under development in JUNO, which allow prompt alert and trigger-less data acquisition of CCSN events. The alert performances of both monitoring systems have been thoroughly studied using simulations. Moreover, once a CCSN is tagged, the system can give fast characterizations, such as directionality and light curve

Detection of the Diffuse Supernova Neutrino Background with JUNO

As an underground multi-purpose neutrino detector with 20 kton liquid scintillator, Jiangmen Underground Neutrino Observatory (JUNO) is competitive with and complementary to the water-Cherenkov detectors on the search for the diffuse supernova neutrino background (DSNB). Typical supernova models predict 2-4 events per year within the optimal observation window in the JUNO detector. The dominant background is from the neutral-current (NC) interaction of atmospheric neutrinos with 12C nuclei, which surpasses the DSNB by more than one order of magnitude. We evaluated the systematic uncertainty of NC background from the spread of a variety of data-driven models and further developed a method to determine NC background within 15\% with {\it{in}} {\it{situ}} measurements after ten years of running. Besides, the NC-like backgrounds can be effectively suppressed by the intrinsic pulse-shape discrimination (PSD) capabilities of liquid scintillators. In this talk, I will present in detail the improvements on NC background uncertainty evaluation, PSD discriminator development, and finally, the potential of DSNB sensitivity in JUNO

Quantitative Mutation Analysis of Genes and Proteins of Major SARS-CoV-2 Variants of Concern and Interest

10.3390/v15051193Viruses1551193-119

COVID-19 Anosmia: High Prevalence, Plural Neuropathogenic Mechanisms, and Scarce Neurotropism of SARS-CoV-2?

Severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) is the causative pathogen of coronavirus disease 2019 (COVID-19). It is known as a respiratory virus, but SARS-CoV-2 appears equally, or even more, infectious for the olfactory epithelium (OE) than for the respiratory epithelium in the nasal cavity. In light of the small area of the OE relative to the respiratory epithelium, the high prevalence of olfactory dysfunctions (ODs) in COVID-19 has been bewildering and has attracted much attention. This review aims to first examine the cytological and molecular biological characteristics of the OE, especially the microvillous apical surfaces of sustentacular cells and the abundant SARS-CoV-2 receptor molecules thereof, that may underlie the high susceptibility of this neuroepithelium to SARS-CoV-2 infection and damages. The possibility of SARS-CoV-2 neurotropism, or the lack of it, is then analyzed with regard to the expression of the receptor (angiotensin-converting enzyme 2) or priming protease (transmembrane serine protease 2), and cellular targets of infection. Neuropathology of COVID-19 in the OE, olfactory bulb, and other related neural structures are also reviewed. Toward the end, we present our perspectives regarding possible mechanisms of SARS-CoV-2 neuropathogenesis and ODs, in the absence of substantial viral infection of neurons. Plausible causes for persistent ODs in some COVID-19 convalescents are also examined