Myopic Loss Aversion and the Equity Premium Puzzle

The equity premium puzzle, first documented by Mehra and Prescott, refers to the empirical fact that stocks have greatly outperformed bonds over the last century. As Mehra and Prescott point out, it appears difficult to explain the magnitude of the equity premium within the usual economics paradigm because the level of risk aversion necessary to justify such a large premium is implausibly large. We offer a new explanation based on Kahneman and Tversky's 'prospect theory'. The explanation has two components. First, investors are assumed to be 'loss averse' meaning they are distinctly more sensitive to losses than to gains. Second, investors are assumed to evaluate their portfolios frequently, even if they have long-term investment goals such as saving for retirement or managing a pension plan. We dub this combination 'myopic loss aversion'. Using simulations we find that the size of the equity premium is consistent with the previously estimated parameters of prospect theory if investors evaluate their portfolios annually. That is, investors appear to choose portfolios as if they were operating with a time horizon of about one year. The same approach is then used to study the size effect. Preliminary results suggest that myopic loss aversion may also have some explanatory power for this anomaly.

Secrecy Capacity Region of Fading Broadcast Channels

The fading broadcast channel with confidential messages (BCC) is investigated, where a source node has common information for two receivers (receivers 1 and 2), and has confidential information intended only for receiver 1. The confidential information needs to be kept as secret as possible from receiver 2. The channel state information (CSI) is assumed to be known at both the transmitter and the receivers. The secrecy capacity region is first established for the parallel Gaussian BCC, and the optimal source power allocations that achieve the boundary of the secrecy capacity region are derived. In particular, the secrecy capacity region is established for the Gaussian case of the Csiszar-Korner BCC model. The secrecy capacity results are then applied to give the ergodic secrecy capacity region for the fading BCC.Comment: Proc. of IEEE International Symposium on Information Theory (ISIT), June 200

MAC with Action-Dependent State Information at One Encoder

Problems dealing with the ability to take an action that affects the states of state-dependent communication channels are of timely interest and importance. Therefore, we extend the study of action-dependent channels, which until now focused on point-to-point models, to multiple-access channels (MAC). In this paper, we consider a two-user, state-dependent MAC, in which one of the encoders, called the informed encoder, is allowed to take an action that affects the formation of the channel states. Two independent messages are to be sent through the channel: a common message known to both encoders and a private message known only to the informed encoder. In addition, the informed encoder has access to the sequence of channel states in a non-causal manner. Our framework generalizes previously evaluated settings of state dependent point-to-point channels with actions and MACs with common messages. We derive a single letter characterization of the capacity region for this setting. Using this general result, we obtain and compute the capacity region for the Gaussian action-dependent MAC. The unique methods used in solving the Gaussian case are then applied to obtain the capacity of the Gaussian action-dependent point-to-point channel; a problem was left open until this work. Finally, we establish some dualities between action-dependent channel coding and source coding problems. Specifically, we obtain a duality between the considered MAC setting and the rate distortion model known as "Successive Refinement with Actions". This is done by developing a set of simple duality principles that enable us to successfully evaluate the outcome of one problem given the other.Comment: 1. Parts of this paper appeared in the IEEE International Symposium on Information Theory (ISIT 2012),Cambridge, MA, US, July 2012 and at the IEEE 27th Convention of Electrical and Electronics Engineers in Israel (IEEEI 2012), Nov. 2012. 2. This work has been supported by the CORNET Consortium Israel Ministry for Industry and Commerc

A simplified analysis of the multigrid V-cycle as a fast elliptic solver

For special model problems, Fourier analysis gives exact convergence rates for the two-grid multigrid cycle and, for more general problems, provides estimates of the two-grid convergence rates via local mode analysis. A method is presented for obtaining mutigrid convergence rate estimates for cycles involving more than two grids (using essentially the same analysis as for the two-grid cycle). For the simple cast of the V-cycle used as a fast Laplace solver on the unit square, the k-grid convergence rate bounds obtained by this method are sharper than the bounds predicted by the variational theory. Both theoretical justification and experimental evidence are presented

Cellular Systems with Full-Duplex Compress-and-Forward Relaying and Cooperative Base Stations

In this paper the advantages provided by multicell processing of signals transmitted by mobile terminals (MTs) which are received via dedicated relay terminals (RTs) are studied. It is assumed that each RT is capable of full-duplex operation and receives the transmission of adjacent relay terminals. Focusing on intra-cell TDMA and non-fading channels, a simplified relay-aided uplink cellular model based on a model introduced by Wyner is considered. Assuming a nomadic application in which the RTs are oblivious to the MTs' codebooks, a form of distributed compress-and-forward (CF) scheme with decoder side information is employed. The per-cell sum-rate of the CF scheme is derived and is given as a solution of a simple fixed point equation. This achievable rate reveals that the CF scheme is able to completely eliminate the inter-relay interference, and it approaches a ``cut-set-like'' upper bound for strong RTs transmission power. The CF rate is also shown to surpass the rate of an amplify-and-forward scheme via numerical calculations for a wide range of the system parameters.Comment: Proceedings of the 2008 IEEE International Symposium on Information Theory, Toronto, ON, Canada, July 6 - 11, 200

New Results on Multiple-Input Multiple-Output Broadcast Channels with Confidential Messages

This paper presents two new results on multiple-input multiple-output (MIMO) Gaussian broadcast channels with confidential messages. First, the problem of the MIMO Gaussian wiretap channel is revisited. A matrix characterization of the capacity-equivocation region is provided, which extends the previous result on the secrecy capacity of the MIMO Gaussian wiretap channel to the general, possibly imperfect secrecy setting. Next, the problem of MIMO Gaussian broadcast channels with two receivers and three independent messages: a common message intended for both receivers, and two confidential messages each intended for one of the receivers but needing to be kept asymptotically perfectly secret from the other, is considered. A precise characterization of the capacity region is provided, generalizing the previous results which considered only two out of three possible messages.Comment: Submitted to the IEEE Transactions on Information Theory, 11 pages, 5 figure