Complementarity Modeling of a Ramsey-Type Equilibrium Problem with Heterogeneous Agents

We contribute to the field of Ramsey-type equilibrium models with heterogeneous agents. To this end, we state such a model in a time-continuous and time-discrete form, which in the latter case leads to a finite-dimensional mixed complementarity problem. We prove the existence of solutions of the latter problem using the theory of variational inequalities and present further properties of its solutions. Finally, we compute the growth dynamics in a calibrated model in which households differ with respect to their relative risk aversion, their discount factors, their initial wealth, and with respect to their interest rates on savings.

No-arbitrage concepts in topological vector lattices

We provide a general framework for no-arbitrage concepts in topological vector lattices, which covers many of the well-known no-arbitrage concepts as particular cases. The main structural condition we impose is that the outcomes of trading strategies with initial wealth zero and those with positive initial wealth have the structure of a convex cone. As one consequence of our approach, the concepts NUPBR, NAA$$_1$$ 1 and NA$$_1$$ 1 may fail to be equivalent in our general setting. Furthermore, we derive abstract versions of the fundamental theorem of asset pricing (FTAP), including an abstract FTAP on Banach function spaces, and investigate when the FTAP is warranted in its classical form with a separating measure. We also consider a financial market with semimartingales which does not need to have a numéraire, and derive results which show the links between the no-arbitrage concepts by only using the theory of topological vector lattices and well-known results from stochastic analysis in a sequence of short proofs.

Mean-entropy uncertain portfolio with risk curve and total mental accounts under multiple background risks

In the previous uncertain portfolio literature on background risk and mental account, only a general background risk and a few kinds of mental accounts were considered. Based on the above limitations, on the one hand, the multiple background risks are defined by linear weighting of different background asset risks in this paper; on the other hand, the total nine kinds of mental accounts are comprehensively considered. Especially, the risk curve is regarded as the risk measurement of different mental accounts for the first time. Under the framework of uncertainty theory, a novel mean-entropy portfolio model with risk curve and total mental accounts under multiple background risks is constructed. In addition, transaction fees, chance constraint, upper and lower limits and initial wealth constraints are also considered in our proposed model. In theory, the equivalent forms of the models with different uncertainty distributions (general, normal and zigzag) are presented by three theorems. Simultaneously, the corresponding concrete expressions of risk curves are obtained by another three theorems. In practice, two numerical examples verify the feasibility and effectiveness of our proposed model. Finally, we can obtain the following unique and meaningful findings: (1) investors will underestimate the potential risk if they ignore the existence of multiple background risks; (2) with the increase of the return threshold, the return of the sub-portfolio will inevitably increase, but investors also bear the risk that the risk curve is higher than the confidence curve at this time.

Inflation and Risky Investments

The paper uses a Walrasian two-period financial market model with informed and uninformed constant absolute risk averse (CARA) rational investors and noise traders. The investors allocate their initial wealth between risky assets and risk-free fiat money. The analysis concentrates on the effects of decreasing value of money, or inflation, on the rational investors’ behavior and the asset market. The main findings are the following: Inflation does not affect the informed investors’ prediction coefficient but makes that of the uninformed investors diminish. Inflation does not affect rational investors’ risk but makes the asset price more sensitive to fundament-based and sentiment-based shocks. Inflation changes the market price of the risky asset rise; while it has no effects on the informed investors’ demand of the risky asset, it does affect the uninformed investors’ demand. Finally, inflation makes the asset market more volatile.

Quantifying Risk Perception: The Entropy Decision Risk Model Utility (EDRM-U)

Risk perception can be quantified in measurable terms of risk aversion and sensitivity. While conducting research on the quantization of programmatic risk, a bridge between positive and normative decision theories was discovered through the application of a novel a priori relationship between objective and subjective probabilities and the application of Bernoulli’s expected utility theory. The Entropy Decision Risk Model (EDRM) derived using the Kullback–Liebler entropy divergence from certainty serves as a translation between objective and subjective probability, referred to as proximity, and has proven its applicability to various positive decision theories related to Prospect Theory. However, EDRM initially assumes the validity of the standard exponential power utility function ubiquitous to positive decision theory models as the magnitude of a choice to isolate and validate proximity. This research modifies the prior model by applying Daniel Bernoulli’s expected utility as the measure of choice magnitude in place of power utility. The revised model, EDRM Utility (EDRM-U), predicts the subject choices for both small and large ranges of values and shows that Prospect Theory’s neutral reference point is actually centered about an assumed initial wealth value, called neutral wealth, that correlates to a power utility exponent value. This hypothesis is confirmed by demonstrating that EDRM-U presents an equivalent or better correlation with prior research in eleven landmark studies of college students spanning more than 26 years and comprising over 300 problems, including those with widely varying values. This research contributes to the fields of risk management and decision engineering by proposing a decision model that behaves according to both positive and normative decision theories and provides measures of risk perception.

The modern tontine

We investigate whether a historical pension concept, the tontine, yields enough innovative potential to extend and improve the prevailing privately funded pension solutions in a modern way. The tontine basically generates an age-increasing cash flow, which can help to match the increasing financing needs at old ages. In contrast to traditional pension products, however, the tontine generates volatile cash flows, which means that the insurance character of the tontine cannot be guaranteed in every situation. By employing Multi Cumulative Prospect Theory (MCPT) we answer the question to what extent tontines can be a complement to or a substitute for traditional annuities. We find that it is only optimal to invest in tontines for a certain range of initial wealth. In addition, we investigate in how far the tontine size, the volatility of individual liquidity needs and expected mortality rates contribute to the demand for tontines.

Optimal Collateralized Contracts

We examine the role of collateral in a dynamic model of optimal credit contracts in which a borrower values both housing and nonhousing consumption. The borrower’s private information about his income is the only friction. An optimal contract is collateralized when in some state, some portion of the borrower’s net worth is forfeited to the lender. We show that optimal contracts are always collateralized. The total value of forfeited assets is decreasing in income, highlighting the role of collateral as a deterrent to manipulation. Some assets—those that generate consumable services—will necessarily be collateralized, while others may not be. Endogenous default arises when the borrower’s initial wealth is low, as with subprime borrowers, and/or his future earnings are highly variable. (JEL D82, D86, G21, G51)

Time Discounting and Wealth Inequality

This paper documents a large association between individuals’ time discounting in incentivized experiments and their positions in the real-life wealth distribution derived from Danish high-quality administrative data for a large sample of middle-aged individuals. The association is stable over time, exists through the wealth distribution and remains large after controlling for education, income profile, school grades, initial wealth, parental wealth, credit constraints, demographics, risk preferences, and additional behavioral parameters. Our results suggest that savings behavior is a driver of the observed association between patience and wealth inequality as predicted by standard savings theory. (JEL C91, D15, D31, E21)

THE EFFECT OF THE ASSUMED INTEREST RATE AND SMOOTHING ON VARIABLE ANNUITIES

In this paper, we consider the risk–return trade-off for variable annuities in a Black–Scholes setting. Our analysis is based on a novel explicit allocation of initial wealth over the payments at various horizons. We investigate the relationship between the optimal consumption problem and the design of variable annuities by deriving the optimal so-called assumed interest rate for an investor with constant relative risk aversion preferences. We investigate the utility loss due to deviations from this. Finally, we show analytically how habit-formation-type smoothing of financial market shocks over the remaining lifetime leads to smaller year-to-year volatility in pension payouts, but to increases in the longer-term volatility.

Performance evaluation of portfolios with fuzzy returns

The existing literature on DEA (Data Envelopment Analysis) for evaluating fuzzy portfolios usually takes risk as an input and return as an output. This assumption is actually not congruent with the real investment process, where the input is the initial wealth and the output is the corresponding terminal wealth. As for the risk and return, which are essentially two indicators derived from the terminal wealth, both should be regarded as outputs. In addition, few studies have employed the diversification model (nonlinear DEA) to estimate the fuzzy portfolio efficiency (PE), despite the fact that there are many studies available within the framework of classical probability theory. Further, the relationship between DEA and diversification models needs to be defined. In this paper, we take the initial wealth as an input, while the return and risk of terminal wealth are taken as desirable and undesirable outputs, respectively. We construct different evaluation models under the fuzzy portfolio framework. The relationships among the evaluation model based on a real frontier, the diversification model and the DEA model are investigated. We show the convergence of the diversification and DEA models under the fuzzy theory framework. Some simulations as well as empirical analysis are presented to further verify the effectiveness of the proposed models. Finally, we check the robustness of the evaluation results by using the bootstrap re-sampling approach.