This model contains concept, equations, and graphical results for venture banking. A system of 27 equations describes the behavior of the venture-bank and underwriter system allowing phase-space type graphs that show where profits and losses occur. These results confirm and expand those obtained from the original spreadsheet based model. An example investment in a castle at a loss is provided to clarify concept. This model requires that all investments are in enterprises that create new utility value. The assessed utility value created is the new money out of which the venture bank and underwriter are paid. The model presented chooses parameters that ensure that the venture-bank experiences losses before the underwriter does. Parameters are: DIN Premium, 0.05; Clawback lien fraction, 0.77; Clawback bonds and equity futures discount, 1.5 x (USA 12 month LIBOR); Range of clawback bonds sold, 0 to 100%; Range of equity futures sold 0 to 70%.

This chapter presents a review of the dividend discount models starting from the basic models (Williams 1938, Gordon and Shapiro 1956) to more recent and complex models (Ghezzi and Piccardi 2003, Barbu et al. 2017, D'Amico and De Blasis 2018) with a focus on the modelling of the dividend process rather than the discounting factor, that is assumed constant in most of the models. The Chapter starts with an introduction of the basic valuation model with some general aspects to consider when performing the computation. Then, Section 1.3 presents the Gordon growth model (Gordon 1962) with some of its extensions (Malkiel 1963, Fuller and Hsia 1984, Molodovsky et al. 1965, Brooks and Helms 1990, Barsky and De Long 1993), and reports some empirical evidence. Extended reviews of the Gordon stock valuation model and its extensions can be found in Kamstra (2003) and Damodaran (2012). In Section 1.4, the focus is directed to more recent advancements which make us of the Markov chain to model the dividend process (Hurley and Johnson 1994, Yao 1997, Hurley and Johnson 1998, Ghezzi and Piccardi 2003, Barbu et al. 2017, D'Amico and De Blasis 2018). The advantage of these models is the possibility to obtain a different valuation that depends on the state of the dividend series, allowing the model to be closer to reality. In addition, these models permit to obtain a measure of the risk of the single stock or a portfolio of stocks.

Using results from neurobiology on perceptual decision making and value-based decision making, the problem of decision making between lotteries is reformulated in an abstract space where uncertain prospects are mapped to corresponding active neuronal representations. This mapping allows us to maximize non-extensive entropy in the new space with some constraints instead of a utility function. To achieve good agreements with behavioral data, the constraints must include at least constraints on the weighted average of the stimulus and on its variance. Both constraints are supported by the adaptability of neuronal responses to an external stimulus. By analogy with thermodynamic and information engines, we discuss the dynamics of choice between two lotteries as they are being processed simultaneously in the brain by rate equations that describe the transfer of attention between lotteries and within the various prospects of each lottery. This model is able to give new insights on risk aversion and on behavioral anomalies not accounted for by Prospect Theory.

I propose creation of a venture bank, able to multiply the capital of a venture capital firm by at least 47 times, without requiring access to the Federal Reserve or other central bank apart from settlement. This concept rests on obtaining default swap instruments on loans in order to create the capital required, and expand Tier 1 and 2 base capital. Profitability depends on overall portfolio performance, availability of equity default swaps, cost of default swap, and the multiple of original capital (MOC) adopted by the venture bank. A new derivative financial instrument, the equity default swap (EDS), to cover loans made as venture investments. An EDS is similar to a credit default swap (CDS) but with some unique features. The features and operation of these new derivative instruments are outlined along with audit requirements. This instrument would be traded on open-outcry exchanges with special features to ensure orderly operation of the market. It is the creation of public markets for EDSs that makes possible the use of public market pricing to indirectly provide a potential market capitalization for the underlying venture-bank investment. Full coverage insulates the venture-bank from losses in most situations, and multiplies profitability quite dramatically in all scenarios. Ten year returns above 20X are attainable. Further, a new feature for EDS derivatives, a clawback lien, closes out the equity default swap. Here it is optimized at 77%, and is to be paid back to the underwriter at a future date to prevent perverse incentive to deliberately fail. This new feature creates an Equity Default Clawback Swap (EDCS) which can be used safely. This proposal also solves an old problem in banking, because it matches the term of the loan with the term of the investment. I show that the venture-bank investment and the EDCS underwriting business are profitable.

The constraints on a continuous growth in a finite environment are formally analyzed, adding the effect of the necessary dynamics of costs. The unavoidable global collapse is deduced. The effect of competition in a growing economic system on the evolution of unequal share of wealth is also analyzed and discussed, showing the necessity of increase of inequalities under the premises of growth and competition.

It is known that the probability is not a conserved quantity in the stock market, given the fact that it corresponds to an open system. In this paper we analyze the flow of probability in this system by expressing the ideal Black-Scholes equation in the Hamiltonian form. We then analyze how the non-conservation of probability affects the stability of the prices of the Stocks. Finally, we find the conditions under which the probability might be conserved in the market, challenging in this way the non-Hermitian nature of the Black-Scholes Hamiltonian.

We propose a new model for regulation to achieve AI safety: global regulatory markets. We first sketch the model in general terms and provide an overview of the costs and benefits of this approach. We then demonstrate how the model might work in practice: responding to the risk of adversarial attacks on AI models employed in commercial drones.

A scenario in which regulators take the drastic step of requiring coverage of all venture bank investment loans using interbank borrowed funds is considered. In this scenario, a minimal amount of default insurance is used, such that Tier 1 and 2 capital requirements are still met. To do this, the default insurance percentage on all investment loans is cut to 3.88%, although the minimum is 2.88%. Results: For a portfolio of 1.31X (ten year total conventional return) or better, at interest rates of 2% or better, the venture bank survives and can have excellent returns. For a portfolio of 1.5X (ten year total conventional return) the bank can have extraordinary returns below 1.5% interest and survive up to 3%. interest. However, if returns fall, or interest rates rise, then venture banks go underwater quite rapidly. Conclusion: Using LIBOR funds limits profitability, and damages stability of the bank, with no visible benefit to any party, thus creating a new systemic risk to the banking system.

Procyclicality of historical risk measure estimation means that one tends to over-estimate future risk when present realized volatility is high and vice versa under-estimate future risk when the realized volatility is low. Out of it different questions arise, relevant for applications and theory: What are the factors which affect the degree of procyclicality? More specifically, how does the choice of risk measure affect this? How does this behaviour vary with the choice of realized volatility estimator? How do different underlying model assumptions influence the pro-cyclical effect? In this paper we consider three different well-known risk measures (Value-at-Risk, Expected Shortfall, Expectile), the r-th absolute centred sample moment, for any integer $r>0$, as realized volatility estimator (this includes the sample variance and the sample mean absolute deviation around the sample mean) and two models (either an iid model or an augmented GARCH($p$,$q$) model). We show that the strength of procyclicality depends on these three factors, the choice of risk measure, the realized volatility estimator and the model considered. But, no matter the choices, the procyclicality will always be present.

When an insurance note is also a derivative a serious problem arises because a derivative must be fulfilled immediately. This feature of derivatives prevents claims processing procedures that screen out ineligible claims. This, in turn, creates a perverse incentive for insured holders of notes to commit acts that result in payment. This problem first surfaced with CDS contracts, which are part of a class of loan insurance I term a default insurance note.

Without an address to this problem, within the average range of returns for a large venture capital portfolio, a venture-bank makes less money the better their investments do, in a continuous function. The highest rate of return is a total loss, 64% more than a top portfolio.

Here, a strategy for removing this perverse incentive is defined, consisting of a clawback lien that returns part of the payment value as a lien on the firm that is the beneficiary of the insurance. This is presented as the final major component for implementing a default insurance note system so that venture-banking can operate to maximum benefit. Removing the perverse incentive also minimizes disincentive for underwriters to deny DIN coverage to new venture capital firms, or to those firms that have historical earnings which are below average.